Global Index

# Coq Reference Manual

# Global Index

+, 9.2 ∣∣, 9.2 *, 3.1.3, 3.2.2 * (command), 7.2.7 +, 3.1.3, 3.2.2 + (command), 7.2.7 -, 3.2.2 - (command), 7.2.7 /, 3.2.2 ‘(…), 2.7.19 ‘{…}, 2.7.19 2-level approach, 8.14.2 ;, 9.2 ;[…∣…∣…], 9.2 <, 3.2.2 <=, 3.2.2 >, 3.2.2 >=, 3.2.2 ?, 8.2.3 ?=, 3.2.2 [>…∣…∣…], 9.2 %, 12.2.2 &, 3.1.4 _, 1.2.11 _CoqProject, 15.2 {, 7.2.6 {A}+{B}, 3.1.4 {x:A ∣ (P x)}, 3.1.4 {x:A & (P x)}, 3.1.4 }, 7.2.6 … : … (ssreflect), 11.5.3 … => … (ssreflect), 11.5.4 … in … (ssreflect), 11.5.1, 11.6.5 @, 2.7.11 :, 9.2 A*B, 3.1.3 A+{B}, 3.1.4 A+B, 3.1.3 Abbreviations, 12.3 Abort, 7.1.6 About, 6.1.1 Absolute names, 2.6.2 Acc, 3.1.6 Acc_inv, 3.1.6 Acc_rect, 3.1.6 Add Field, 8.16.4, 25.8 Add LoadPath, 6.6.3 Add ML Path, 6.6.7 Add Morphism, 27.2.4 Add Parametric Morphism, 27.1.2 Add Parametric Relation, 27.1.2 Add Printing Coercion, 18.8.2 Add Printing If ident, 2.2.4 Add Printing Let ident, 2.2.4 Add Rec LoadPath, 6.6.4 Add Rec ML Path, 6.6.8 Add Relation, 27.1.2 Add Ring, 8.16.3, 25.5 Add Setoid, 27.2.4 Admit Obligations, 24.2 Admitted, 1.3.5, 7.1.3 Arguments, 2.7.4, 2.7.4, 2.7.5, 2.7.12, 8.7.4, 12.2.2 Arithmetical notations, 3.2.2 Arity, 4.5.2 Associativity, 12.1.2 Asymmetric Patterns, 17.2 Asynchronous and Parallel Proof Processing presentation, 28 Automatic Coercions Import, 18.11 Automatic Introduction, 7.4.3 Axiom, 1.3.1 Axiom (and coercions), 18.6.1 abstract, 9.2 abstract: … (ssreflect), 11.5.3 abstractions, 1.2.7 absurd, 3.1.2, 8.4.6 absurd_set, 3.1.4 admit, 8.4.5 algebraic universe, 4.1.1 all, 3.1.2 and, 3.1.2 and_rect, 3.1.4 app, 3.2.5 appcontext in pattern, 9.2 applications, 1.2.9 apply, 8.2.4 apply … in, 8.2.5 apply … with, 8.2.4 apply/… (ssreflect), 11.9.6 apply/…/… (ssreflect), 11.9.7 apply: … (ssreflect), 11.5.2 arity of inductive type, 4.5 assert, 8.4.1 assert as, 8.4.1 assert by, 8.4.1 assumption global, 4.2 local, 4.2 assumption, 8.2.2 auto, 8.8.1 autoapply, 20.6.6 autorewrite, 8.8.4 autounfold, 8.8.3 Back, 6.7.2 BackTo, 6.7.3 Backtrack, 6.7.3 Bad Magic Number, 6.5.1 Bind Scope, 12.2.2 Binding list, 8.1.3 BNF metasyntax, 1 Boolean Equality Schemes, 13.1.1 Bracketing Last Introduction Pattern, 8.3.2 Bullet Behavior, 7.2.8 Bullets, 7.2.7 β-reduction, 4.3, 4.3 binders, 1.2.6 bool, 3.1.3 bool_choice, 3.1.4 btauto, 8.16.1 by … (ssreflect), 11.6.2 byte-code, 14.1 Calculus of Inductive Constructions, 4 Canonical Structure, 2.7.17 Canonical Structures presentation, 19 Case Analysis Schemes, 13.1.1 Cases, 17 Cast, 1.2.10 Cd, 6.6.2 Check, 6.3.1 Choice, 3.1.4 Choice2, 3.1.4 CIC, 4 Class, 20.6.1 Clauses, 8.7 Close Scope, 12.2.1 Coercion, 2.8, 18.6.1, 18.6.1 Coercions, 2.8 and modules, 18.11 and records, 18.9 and sections, 18.10 classes, 18.2 Funclass, 18.3 identity, 18.4 inheritance graph, 18.5 presentation, 18 Sortclass, 18.3 CoFixpoint, 1.3.4, 1.3.5 CoFixpoint … where …, 12.1.8 CoInductive, 1.3.3, 2.1 CoInductive (and coercions), 18.6.1 Collection, 7.1.5 Combined Scheme, 13.1.2 Comments, 1.1 Compiled files, 6.5 Compute, 6.3.3 Congruence Verbose, 8.10.5 Conjecture, 1.3.1 Connectives, 3.1.2 Constant, 1.3.2 Constraint, 29.7.2 Context, 20.6.4 Contextual Implicit, 2.7.8 Contributions, 3.3 Conversion rules, 4.3 Conversion tactics, 8.7 Corollary, 1.3.5 CreateHintDb, 8.9.1 Cumulative, 29.3 case, 8.5.1 case: … (ssreflect), 11.5.2 case: … / … (ssreflect), 11.5.6 case_eq, 8.5.1 (…: …), 1.2.10 cbn, 8.7.4 cbv, 8.7.1 change, 8.6.5 change … in, 8.6.5 classical_left, 8.15.1 classical_right, 8.15.1 clear, 8.3.3 clear dependent, 8.3.3 clearbody, 8.3.3 cofix, 8.5.10 compare, 8.13.2 compute, 8.7.1, 8.7.1 congruence, 8.10.5 conj, 3.1.2 constr_eq, 8.11.1 constructor, 8.2.6 context in expression, 9.2 in pattern, 9.2 context of parameters, 4.5 contradict, 8.4.8 contradiction, 8.4.7 coq-tex, 15.5 coq_Makefile, 15.2 coqc, 14 coqchk, 14 coqdep, 15.3 coqdoc, 15.4 coqide, 16 coqmktop, 15.1 coqtop, 14 cut, 8.4.1 cutrewrite, 8.6.2, 8.6.2 cycle, 8.17.1 Datatypes, 3.1.3 Debug Auto, 8.8.1 Debug Cbv, 8.7.1 Debug Eauto, 8.8.2 Debug RAKAM, 8.7.4 Debug Trivial, 8.8.1 Debugger, 15.1 Decidable Equality Schemes, 13.1.1 Declarations, 1.3.1 Declare Implicit Tactic, 8.9.7 Declare Instance, 20.6.2 Declare Left Step, 8.6.4 Declare ML Module, 6.5.3 Declare Module, 2.5.7 Declare Right Step, 8.6.4 Default Goal Selector, 8.1.1 Default Proof Using, 7.1.5 Default Timeout, 6.8.6, 6.8.7, 6.8.8 Defined, 1.3.5, 7.1.2 Definition, 1.3.2 Definitions, 1.3.2 Delimit Scope, 12.2.2 Dependencies, 15.3 Derive, 30.1.1 Derive Dependent Inversion, 13.3 Derive Dependent Inversion_clear, 13.3 Derive Inversion, 13.3 Derive Inversion_clear, 13.3 Disjunctive/conjunctive introduction patterns, 8.3.2, 8.3.2 Drop, 6.8.2 decide equality, 8.13.1 declaration global, 4.2 local, 4.2 decompose, 8.3.8 decompose record, 8.3.8 decompose sum, 8.3.8 definition global, 4.2 inductive, 4.5 local, 4.2 δ-reduction, 1.3.2, 4.3, 4.3 dependent destruction, 8.5.4 dependent induction, 8.5.4 dependent induction … generalizing, 8.5.4 dependent inversion, 8.5.8 dependent inversion … as , 8.5.8 dependent inversion … as … with, 8.5.8 dependent inversion … with, 8.5.8 dependent inversion_clear, 8.5.8 dependent inversion_clear … as, 8.5.8 dependent inversion_clear … as … with, 8.5.8 dependent inversion_clear … with, 8.5.8 dependent rewrite ->, 8.13.4 dependent rewrite <-, 8.13.4 destruct, 8.5.1 dintuition, 8.10.2 discriminate, 8.5.6 discrR, 3.2.4 do, 9.2 do … [ … ] (ssreflect), 11.6.4 double induction, 8.5.3 dtauto, 8.10.1 Elimination Empty elimination, 4.5.3 Singleton elimination, 4.5.3 Elimination Schemes, 13.1.1 Elimination sorts, 4.5.3 Emacs, 15.6 End, 2.4.2, 2.5.2, 2.5.5 Environment, 1.3.1, 1.3.2 Environment variables, 14.3.2 Equality, 3.1.2 Equality introduction patterns, 8.3.2 Eval, 6.3.2 Example, 1.3.2 Exc, 3.1.4 Existential, 7.1.7 Existing Class, 20.6.1 Existing Instance, 20.6.3 Existing Instances, 20.6.3 Explicitly given implicit arguments, 2.7.11 Export, 2.5.8 Extract Constant, 23.2.4 Extract Inductive, 23.2.4 Extraction, 23 Extraction, 6.3.4, 23.1 Extraction AutoInline, 23.2.2 Extraction Blacklist, 23.2.5 Extraction Conservative Types, 23.2.2 Extraction Implicit, 23.2.3 Extraction Inline, 23.2.2 Extraction KeepSingleton, 23.2.2 Extraction Language, 23.2.1 Extraction Library, 23.1 Extraction NoInline, 23.2.2 Extraction Optimize, 23.2.2 Extraction SafeImplicits, 23.2.3 eapply, 8.2.4 eapply … in, 8.2.5 eassert, 8.4.1 eassert as, 8.4.1 eassert by, 8.4.1 eassumption, 8.2.2 easy, 8.8.5 eauto, 8.8.2 ecase, 8.5.1 econstructor, 8.2.6 edestruct, 8.5.1 ediscriminate, 8.5.6 eelim, 8.5.2 eenough, 8.4.1 eenough as, 8.4.1 eenough by, 8.4.1 eexact, 8.2.1 eexists, 8.2.6 einduction, 8.5.2 einjection, 8.5.7 eleft, 8.2.6 elim … using, 8.5.2 elim/… (ssreflect), 11.9.1 elim: … (ssreflect), 11.5.2 elimtype, 8.5.2 enough, 8.4.1, 8.4.1 enough as, 8.4.1 enough by, 8.4.1, 8.4.1, 8.4.1 epose, 8.3.7 epose proof, 8.4.1 eq, 3.1.2 eq_add_S, 3.1.5 eq_ind_r, 3.1.2 eq_rec_r, 3.1.2 eq_rect, 3.1.2, 3.1.4 eq_rect_r, 3.1.2 eq_refl, 3.1.2 eq_S, 3.1.5 eq_sym, 3.1.2 eq_trans, 3.1.2 eremember, 8.3.7 erewrite, 8.6.1 eright, 8.2.6 error, 3.1.4 eset, 8.3.7 esimplify_eq, 8.13.3 esplit, 8.2.6 η-expansion, 4.3 eval in Ltac, 9.2 evar, 8.4.3 ex, 3.1.2 ex2, 3.1.2 ex_intro, 3.1.2 ex_intro2, 3.1.2 exact, 8.2.1 exactly_once, 9.2 exfalso, 8.4.9 exist, 3.1.4 exist2, 3.1.4 exists, 3.1.2, 8.2.6 exists2, 3.1.2 existT, 3.1.4 existT2, 3.1.4 Fact, 1.3.5 Fail, 6.8.9 False, 3.1.2 False_rec, 3.1.4 False_rect, 3.1.4 Firstorder Depth, 8.10.4 Firstorder Solver, 8.10.4 Fix, 4.5.4 Fix_F, 3.1.6 Fix_F_eq, 3.1.6 Fix_F_inv, 3.1.6 Fixpoint, 1.3.4, 1.3.5 Fixpoint … where …, 12.1.8 Focus, 7.2.3 From Require, 6.5.1 Function, 2.3 Functional Scheme, 13.2 f_equal, 3.1.2, 8.12.1 f_equali, 3.1.2 fail, 9.2 false, 3.1.3 field, 8.16.4, 25.7 field_simplify, 8.16.4, 25.7 field_simplify_eq, 8.16.4, 25.7 first, 9.2 first … last (ssreflect), 11.6.3 firstorder, 8.10.4 firstorder tactic, 8.10.4 firstorder using, 8.10.4 firstorder with, 8.10.4 fix, 8.5.9 fix identi{…}, 1.2.14 fix_eq, 3.1.6 flat_map, 3.2.5 fold, 8.7.6 fold_left, 3.2.5 fold_right, 3.2.5 forall …, …, 1.2.8 form, 1.2.5 fourier, 8.16.5 fresh in Ltac, 9.2 fst, 3.1.3 fun in Ltac, 9.2 fun …=> …, 1.2.7 function_scope, 12.2.4 functional induction, 8.5.5, 13.2 functional inversion, 8.14.1 Gallina, 1, 2 Generalizable Variables, 2.7.19 Global, 6.11.1 Global Arguments, 2.7.4, 2.7.5 Global environment, 4.2 Global Set, 6.2.4 Global Unset, 6.2.2, 6.2.5 Goal, 7.1.1 Goal clauses, 8.7 Grab Existential Variables, 7.1.8 Guarded, 7.3.2 gallina, 15.7 ge, 3.1.5 generalize, 8.4.2 generalize dependent, 8.4.2 gfail, 9.2 give_up, 8.4.5, 8.17.6 goal, 8 gt, 3.1.5 guard in Ltac, 9.2 Head normal form, 4.4 Hide Obligations, 24.2 Hint, 8.9.1 Hint Constructors, 8.9.1 Hint Cut, 8.9.1 Hint Extern, 8.9.1 Hint Immediate, 8.9.1 Hint Mode, 8.9.1 Hint Opaque, 8.9.1 Hint Resolve, 8.9.1 Hint Rewrite, 8.9.5 Hint Transparent, 8.9.1 Hint Unfold, 8.9.1 Hint View (ssreflect), 11.9.8 Hints databases, 8.9.1 Hypotheses, 1.3.1 Hypothesis, 1.3.1 Hypothesis (and coercions), 18.6.1 Hyps Limit, 7.4.1, 7.4.2 has_evar, 8.11.4 have: … (ssreflect), 11.6.6 have: … := … (ssreflect), 11.6.6 head, 3.2.5 hnf, 8.7.3 I, 3.1.2 Identity Coercion, 18.6.2 IF_then_else, 3.1.2 Implicit Arguments, 2.7.6 Implicit arguments, 2.7 Implicit Types, 2.7.18 Import, 2.5.8 Include, 2.5.1, 2.5.4 Inductive, 1.3.3, 1.3.3, 2.1 Inductive (and coercions), 18.6.1 Inductive … where …, 12.1.8 Inductive definitions, 1.3.3 Infix, 12.1.6 Info, 9.4.1 Info Auto, 8.8.1 Info Eauto, 8.8.2 Info Level, 9.4.1 Info Trivial, 8.8.1 Inline, 2.5.4 Inspect, 6.1.2 Instance, 20.6.2 Interpretation scopes, 12.2 Introduction patterns, 8.3.2 Intuition Iff Unfolding, 8.10.2 Intuition Negation Unfolding, 8.10.2 IsSucc, 3.1.5 ident, 1.1 identity, 3.1.3 idtac, 9.2 if ... then ... else, 2.2.2 iff, 3.1.2 induction, 8.5.2 injection, 8.5.7 injection … as, 8.5.7 inl, 3.1.3 inleft, 3.1.4 inr, 3.1.3 inright, 3.1.4 instantiate, 8.4.4 integer, 1.1 intro, 8.3.1 intro after, 8.3.1 intro at bottom, 8.3.1 intro at top, 8.3.1 intro before, 8.3.1 intros, 8.3.1 intros intro_pattern, 8.3.2 intros until, 8.3.1, 8.3.1 intuition, 8.10.2 inversion, 8.5.8 inversion … as, 8.5.8 inversion … as … in, 8.5.8 inversion … in, 8.5.8 inversion … using, 8.5.8, 13.3 inversion … using … in, 8.5.8 inversion_clear, 8.5.8 inversion_clear … as, 8.5.8 inversion_clear … as … in, 8.5.8 inversion_clear … in, 8.5.8 inversion_sigma, 8.5.8 ι-reduction, 4.3, 4.3, 4.5.3, 4.5.4 is_evar, 8.11.3 is_var, 8.11.5 Keep Proof Equalities, 8.5.7, 8.5.8 LATEX, 15.5 Lemma, 1.3.5 Let, 1.3.2 Let-in definitions, 1.2.12 Lexical conventions, 1.1 Libraries, 2.6.1 | Load, 6.4.1 Load Verbose, 6.4.1 Loadpath, 2.6.3 Local, 6.11.1 Local Arguments, 2.7.4, 2.7.5 Local Axiom, 1.3.1 Local Coercion, 18.6.1, 18.6.1 Local context, 4.2 Local Definition, 1.3.2 Local Set, 6.2.4 Local Strategy, 6.10.3 Local Unset, 6.2.2, 6.2.5 Locate, 6.3.10, 12.1.10 Locate File, 6.6.10 Locate Library, 6.6.11 Locate Ltac, 6.3.10 Locate Module, 2.5.11 Locate Term, 6.3.10 Logical paths, 2.6.3 Loose Hint Behavior, 8.9.6 Ltac eval, 9.2 fresh, 9.2 fun, 9.2 guard, 9.2 lazymatch, 9.2 lazymatch goal, 9.2 lazymatch reverse goal, 9.2 let, 9.2 let rec, 9.2 match, 9.2 match goal, 9.2 match reverse goal, 9.2 multimatch, 9.2 multimatch goal, 9.2 multimatch reverse goal, 9.2 numgoals, 9.2 type of, 9.2 type_term, 9.2 uconstr, 9.2 Ltac, 9.3 Ltac Batch Debug, 9.4.2 Ltac Debug, 9.4.2 Ltac Profiling, 9.4.3 λ-calculus, 4.1.2 lapply, 8.2.4 last … first (ssreflect), 11.6.3 lazy, 8.7.1 lazymatch in Ltac, 9.2 lazymatch goal in Ltac, 9.2 lazymatch reverse goal in Ltac, 9.2 le, 3.1.5 le_n, 3.1.5 le_S, 3.1.5 left, 3.1.4, 8.2.6 length, 3.2.5 let in Ltac, 9.2 let …:= …in …, 1.2.12 let ’... in, 2.2.3 let ... in, 2.2.3 let rec in Ltac, 9.2 let-in, 1.2.12 lia, 22.1, 22.4 local context, 7 lra, 22.1 lt, 3.1.5 ltac:( …), 2.11.2 Makefile, 15.2 Man pages, 15.8 Maximal Implicit Insertion, 2.7.10 ML-like patterns, 2.2.1, 17 Module, 2.5.1, 2.5.3 Module Type, 2.5.4 Modules, 2.5 Monomorphic, 29.2 map, 3.2.5 match in Ltac, 9.2 match…with…end, 1.2.13, 2.2, 4.5.3 match goal in Ltac, 9.2 match reverse goal in Ltac, 9.2 mod, 3.2.2 move, 8.3.5 move (ssreflect), 11.5.2 move eq : … (ssreflect), 11.5.5 move/… (ssreflect), 11.9.2, 11.9.2, 11.9.6 move: … (ssreflect), 11.5.1 move: … => … (ssreflect), 11.5.1 move=> … (ssreflect), 11.5.1 mult, 3.1.5 mult_n_O, 3.1.5 mult_n_Sm, 3.1.5 multimatch in Ltac, 9.2 multimatch goal in Ltac, 9.2 multimatch reverse goal in Ltac, 9.2 Naming introduction patterns, 8.3.2 Next Obligation, 24.2 NonCumulative, 29.3 None, 3.1.3 Nonrecursive Elimination Schemes, 13.1.1 Normal form, 4.4 Notation, 12.1, 12.3 Notations for lists, 3.2.5 Notations for real numbers, 3.2.4 n_Sn, 3.1.5 nat, 3.1.3 nat_case, 3.1.5 nat_double_ind, 3.1.5 nat_scope, 3.2.3 native code, 14.1 native_compute, 8.7.1, 8.7.1 nia, 22.1, 22.6 not, 3.1.2 not_eq_S, 3.1.5 notT, 3.1.7 notypeclasses refine, 8.2.3 now, 8.8.5 nra, 22.1, 22.5 nsatz, 26.1 nth, 3.2.5 num, 1.1 numgoals in Ltac, 9.2 O, 3.1.3 O_S, 3.1.5 Obligation, 24.2 Obligation Tactic, 24.2 Obligations, 24.2 Occurrences clauses, 8.1.4 Omega Action, 21.3 Omega System, 21.3 Omega UseLocalDefs, 21.3 Opaque, 6.10.1 Open Scope, 12.2.1 Optimize Heap, 7.5 Optimize Proof, 7.5 Options of the command line, 14.3.3 omega, 8.16.2, 21.1 once, 9.2 option, 3.1.3 or, 3.1.2 or_introl, 3.1.2 or_intror, 3.1.2 Parameter, 1.3.1 Parameter (and coercions), 18.6.1 Parameters, 1.3.1 Parsing Explicit, 2.7.16 Peano’s arithmetic, 3.2.3 Physical paths, 2.6.3 Polymorphic, 29.2 Polymorphic Inductive Cumulativity, 29.3 Positivity, 4.5.2 Precedences, 12.1.2 Preterm, 24.2 Primitive Projections, 2.1.1 Primitive projections, 2.1.1 Print, 6.1.1 Print All, 6.1.2 Print All Dependencies, 6.3.5 Print Assumptions, 6.3.5 Print Canonical Projections, 2.7.17 Print Classes, 18.7.1 Print Coercion Paths, 18.7.4 Print Coercions, 18.7.2 Print Extraction Inline, 23.2.2 Print Fields, 8.16.4 Print Grammar constr, 12.1.4 Print Grammar pattern, 12.1.4 Print Graph, 18.7.3 Print Hint, 8.9.4 Print HintDb, 8.9.4 Print Implicit, 2.7.13 Print Libraries, 6.5.2 Print LoadPath, 6.6.6 Print Ltac, 9.3.2 Print Ltac Signatures, 9.3.2 Print ML Modules, 6.5.4 Print ML Path, 6.6.9 Print Module, 2.5.9 Print Module Type, 2.5.10 Print Opaque Dependencies, 6.3.5 Print Options, 6.2.8 Print Rings, 8.16.3 Print Scope, 12.2.6 Print Scopes, 12.2.6 Print Section, 6.1.2 Print Sorted Universes, 2.10 Print Strategies, 6.10.4 Print Strategy, 6.10.4 Print Table Printing If, 2.2.4 Print Table Printing Let, 2.2.4 Print Tables, 6.2.8 Print Term, 6.1.1 Print Transparent Dependencies, 6.3.5 Print Universes, 2.10 Print Visibility, 12.2.6 Printing All, 2.9 Printing Coercions, 18.8.1 Printing Compact Contexts, 6.9.12, 6.9.13, 6.9.14 Printing Dependent Evars Line, 6.9.18, 6.9.19 Printing Depth, 6.9.9, 6.9.10, 6.9.11 Printing Existential Instances, 2.11.1 Printing Implicit, 2.7.14 Printing Implicit Defensive, 2.7.14 Printing Matching, 2.2.4 Printing Notations, 12.1.9 Printing Primitive Projection Compatibility, 2.1.1 Printing Primitive Projection Parameters, 2.1.1 Printing Projections, 2.1 Printing Records, 2.1 Printing Synth, 2.2.4 Printing Unfocused, 6.9.15, 6.9.16, 6.9.17 Printing Universes, 2.10 Printing Width, 6.9.6, 6.9.7, 6.9.8 Printing Wildcard, 2.2.4 Program, 24 Program Generalized Coercion, 24.1 Program Cases, 24.1 Program Definition, 24.1.2 Program Fixpoint, 24.1.3 Program Instance, 20.1, 20.6.2 Program Lemma, 24.1.4 Programming, 3.1.3 Prompt, 7 Proof, 1.3.5, 7.1.4 Proof editing, 7 Proof General, 15.6.2 Proof term, 7 Proof using, 7.1.5 Proof with, 8.9.7 Prop, 1.2.5, 4.1.1 Proposition, 1.3.5 Pwd, 6.6.1 pair, 3.1.3 pairT, 3.1.7 pattern, 8.7.7 plus, 3.1.5 plus_n_O, 3.1.5 plus_n_Sm, 3.1.5 pose, 8.3.7 pose … := … (ssreflect), 11.4.1 pose cofix … := … (ssreflect), 11.4.1 pose fix … := … (ssreflect), 11.4.1 pose proof, 8.4.1 pred, 3.1.5 pred_Sn, 3.1.5 prod, 3.1.3 prodT, 3.1.7 products, 1.2.8, 4.1.2 progress, 9.2 proj1, 3.1.2 proj2, 3.1.2 projT1, 3.1.4 projT2, 3.1.4 psatz, 22.1 Qed, 1.3.5, 7.1.2 Qed exporting, 9.2 Qualified identifiers, 2.6.2 Quantifiers, 3.1.2 Quit, 6.8.1 qualid, 2.7.11 quote, 8.14.2, 10.3 Record, 2.1 Record Elimination Schemes, 13.1.1 Recursion, 3.1.6 Recursive arguments, 4.5.4 Recursive Extraction, 23.1 Recursive Extraction Library, 23.1 Redirect, 6.8.4 Refine Instance Mode, 20.6.20 Refolding Reduction, 8.7.4 Regular Subst Tactic, 8.6.3 Remark, 1.3.5 Remove Hints, 8.9.3 Remove LoadPath, 6.6.5 Remove Printing Coercion, 18.8.2 Remove Printing If ident, 2.2.4 Remove Printing Let ident, 2.2.4 Require, 6.5.1 Require Export, 6.5.1 Require Import, 6.5.1 Reserved Notation, 12.1.7 Reset, 6.7.1 Reset Extraction Inline, 23.2.2 Reset Initial, 6.7.1 Reset Ltac Profile, 9.4.3 Resource file, 14.3.1 Restart, 7.2.2 Reversible Pattern Implicit, 2.7.9 Rewriting Schemes, 13.1.1 red, 8.7.2 refine, 8.2.3 refl_identity, 3.1.3 reflexivity, 8.12.2 remember, 8.3.7 rename, 8.3.6 repeat, 9.2 replace … with, 8.6.2 rev, 3.2.5 revert, 8.3.4 revert dependent, 8.3.4 revgoals, 8.17.3 rewrite, 8.6.1 rewrite ->, 8.6.1 rewrite <-, 8.6.1 rewrite … at, 8.6.1 rewrite … by, 8.6.1 rewrite … in, 8.6.1 rewrite … (ssreflect), 11.7 rewrite_strat, 27.4.2 right, 3.1.4, 8.2.6 ring, 8.16.3, 25, 25.4 ring_simplify, 8.16.3, 25.4 rtauto, 8.10.3 S, 3.1.3 Scheme, 13.1 Scheme Equality, 13.1 Schemes, 13.1 Script file, 6.4 Search, 6.3.6 Search … (ssreflect), 11.10 Search Output Name Only, 6.9.4, 6.9.5 Search Output Name Only mode, 6.9.4 SearchAbout, 6.3.6 SearchHead, 6.3.7 SearchPattern, 6.3.8 SearchRewrite, 6.3.9 Section, 2.4.1 Sections, 2.4 Separate Extraction, 23.1 Set, 6.2.1, 6.2.4 Set, 1.2.5, 4.1.1 Short Module Printing, 2.5.9 Show, 7.3.1 Show Conjectures, 7.3.1 Show Existentials, 7.3.1 Show Intro, 7.3.1 Show Intros, 7.3.1 Show Ltac Profile, 9.4.3 Show Match, 7.3.1 Show Obligation Tactic, 24.2 Show Proof, 7.3.1 Show Script, 7.3.1 Show Universes, 7.3.1 Shrink Abstract, 9.2 Shrink Obligations, 24.2 Silent, 6.9.1, 6.9.2 Silent mode, 6.9.1 Solve Obligations, 24.2 Some, 3.1.3 Sorts, 1.2.5, 1.2.5, 4.1.1 Stable Omega, 21.3 Strategy, 6.10.3 Strict Implicit, 2.7.7 Strict Universe Declaration, 29.7.4 Strongly Strict Implicit, 2.7.7 Structural Injection, 8.5.7 Structure, 18.9 SubClass, 18.6.2 Substitution, 4.1.2 Subtyping rules, 4.4 Suggest Proof Using, 7.1.5 set, 8.3.7 set … := … (ssreflect), 11.4.2 setoid_reflexivity, 27.2.2 setoid_replace, 27.2.2 setoid_rewrite, 27.2.2 setoid_symmetry, 27.2.2 setoid_transitivity, 27.2.2 shelve, 8.17.4 shelve_unifiable, 8.17.4 sig, 3.1.4 sig2, 3.1.4 sigT, 3.1.4 sigT2, 3.1.4 simpl, 8.7.4 simpl … in, 8.7.4 simple notypeclasses refine, 8.2.3 simple apply, 8.2.4 simple apply … in, 8.2.5 simple destruct, 8.5.1 simple eapply … in, 8.2.5 simple induction, 8.5.2 simple inversion, 8.5.8 simple inversion … as, 8.5.8 simple refine, 8.2.3 simplify_eq, 8.13.3 snd, 3.1.3 solve, 9.2 sort, 1.2.1 specialize, 8.4.1 specif, 1.2.5 split, 8.2.6 split_Rabs, 3.2.4 split_Rmult, 3.2.4 start ltac profiling, 9.4.3 stepl, 8.6.4 stepr, 8.6.4 stop ltac profiling, 9.4.3 string, 1.1 subgoal, 8 subst, 8.6.3 suff: … (ssreflect), 11.6.6 suffices: … (ssreflect), 11.6.6 sum, 3.1.3 sumbool, 3.1.4 sumor, 3.1.4 swap, 8.17.2 sym_not_eq, 3.1.2 symmetry, 8.12.3 symmetry in, 8.12.3 Tactic Compat Context, 9.2 Tactic macros, 8.18 Tactic Notation, 12.4 Tacticals, 9.2 :, 9.2 tactic1; tactic2, 9.2 tactic0;[tactic1∣…∣tacticn], 9.2 tactic0;[tactic1∣…∣tacticn], 9.2 abstract, 9.2 do, 9.2 exactly_once, 9.2 fail, 9.2 first, 9.2 gfail, 9.2 idtac, 9.2 once, 9.2 +, 9.2 ∣∣, 9.2 repeat, 9.2 solve, 9.2 time, 9.2 timeout, 9.2 transparent_abstract, 9.2 try, 9.2 tryif, 9.2 Tactics, 8 Template polymorphism, 4.5.2 Terms, 1.2 Test, 6.2.3, 6.2.6 Test Printing If for ident, 2.2.4 Test Printing Let for ident, 2.2.4 Theorem, 1.3.5, 7.1 Theories, 3 Time, 6.8.3 Timeout, 6.8.5 Transparent, 6.10.2 Transparent Obligations, 24.2 True, 3.1.2 Type, 1.2.5, 4.1.1 Typeclass Resolution After Apply, 20.6.13 Typeclass Resolution For Conversion, 20.6.14 Typeclasses Debug, 20.6.19 Typeclasses Debug Verbosity, 20.6.19 Typeclasses Dependency Order, 20.6.8 Typeclasses eauto, 20.6.18 Typeclasses Filtered Unification, 20.6.9 Typeclasses Legacy Resolution, 20.6.10 Typeclasses Limit Intros, 20.6.12 Typeclasses Modulo Eta, 20.6.11 Typeclasses Opaque, 20.6.7 Typeclasses Strict Resolution, 20.6.15 Typeclasses Transparent, 20.6.7 Typeclasses Unique Instances, 20.6.17 Typeclasses Unique Solutions, 20.6.16 Typing rules, 4.2 App, 4.2, 8.4.1 Ax-Prop, 4.2 Ax-Set, 4.2 Ax-Type, 4.2 Const, 4.2 Constr, 4.5.1 Conv, 4.4, 8.3.1, 8.6.5 Fix, 4.5.4 Ind, 4.5.1 Lam, 4.2, 8.3.1 Let, 4.2, 8.3.1 match, 4.5.3 Prod (impredicative Set), 4.8 Prod-Prop, 4.2 Prod-Set, 4.2 Prod-Type, 4.2 Var, 4.2 tactic, 8.1 tail, 3.2.5 tauto, 8.10.1 term, 1.2.1 time, 9.2 timeout, 9.2 transitivity, 8.12.4 transparent_abstract, 9.2 trivial, 8.8.1 true, 3.1.3 try, 9.2 tryif, 9.2 tt, 3.1.3 type, 1.2.2 type of in Ltac, 9.2 type of constructor, 4.5.2, 4.5.2 type_scope, 12.2.3 type_term in Ltac, 9.2 typeclasses eauto, 20.6.5 Undelimit Scope, 12.2.2 Undo, 7.2.1 Unfocus, 7.2.4 Unfocused, 7.2.5 Universal Lemma Under Conjunction, 8.2.4 Universe, 29.7.1 Universe Minimization ToSet, 29.6 Universe Polymorphism, 29.2 Universes presentation, 29 Unset, 6.2.2, 6.2.5 Unshelve, 8.17.5 uconstr in Ltac, 9.2 unfold, 8.7.5 unfold …in, 8.7.5 unify, 8.11.2 unit, 3.1.3 Variable, 1.3.1 Variable (and coercions), 18.6.1 Variables, 1.3.1 Variant, 1.3.3 value, 3.1.4 variable, 4.2 vm_compute, 8.7.1, 8.7.1 Warnings, 6.9.3 Well founded induction, 3.1.6 Well foundedness, 3.1.6 well_founded, 3.1.6 without loss: … / … (ssreflect), 11.6.6 wlog: … / … (ssreflect), 11.6.6 ζ-reduction, 4.3, 4.3