instruction stringclasses 1
value | input stringlengths 876 13.9k | output stringlengths 1 354 |
|---|---|---|
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance NoByz : NoByzantine.
<Previous context>:
Require Import Utf8.
Require Import Reals.
Require Import SetoidDec.
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Util.Bijection.
Require Import Pactole.Util.Fin.
Require Import Pa... | Proof using . |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance NoByz : NoByzantine.
<Previous context>:
Require Import Utf8.
Require Import Reals.
Require Import SetoidDec.
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Util.Bijection.
Require Import Pactole.Util.Fin.
Require Import Pa... | now split. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance NoByz : NoByzantine.
<Previous context>:
Require Import Utf8.
Require Import Reals.
Require Import SetoidDec.
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Util.Bijection.
Require Import Pactole.Util.Fin.
Require Import Pa... | Qed. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance Update : RigidSetting.
<Previous context>:
Require Import Utf8.
Require Import Reals.
Require Import SetoidDec.
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Util.Bijection.
Require Import Pactole.Util.Fin.
Require Import ... | Proof using . |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance Update : RigidSetting.
<Previous context>:
Require Import Utf8.
Require Import Reals.
Require Import SetoidDec.
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Util.Bijection.
Require Import Pactole.Util.Fin.
Require Import ... | split. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance Update : RigidSetting.
<Previous context>:
Require Import Utf8.
Require Import Reals.
Require Import SetoidDec.
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Util.Bijection.
Require Import Pactole.Util.Fin.
Require Import ... | now intros. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance Update : RigidSetting.
<Previous context>:
Require Import Utf8.
Require Import Reals.
Require Import SetoidDec.
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Util.Bijection.
Require Import Pactole.Util.Fin.
Require Import ... | Qed. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Lemma obs_non_empty : forall config pt, obs_from_config config pt =/= @empty location _ _ _.
<Previous context>:
Require Import Utf8.
Require Import Reals.
Require Import SetoidDec.
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Uti... | Proof using ltc_0_k. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Lemma obs_non_empty : forall config pt, obs_from_config config pt =/= @empty location _ _ _.
<Previous context>:
Require Import Utf8.
Require Import Reals.
Require Import SetoidDec.
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Uti... | intros config pt. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Lemma obs_non_empty : forall config pt, obs_from_config config pt =/= @empty location _ _ _.
<Previous context>:
Require Import Utf8.
Require Import Reals.
Require Import SetoidDec.
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Uti... | rewrite obs_from_config_ignore_snd. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Lemma obs_non_empty : forall config pt, obs_from_config config pt =/= @empty location _ _ _.
<Previous context>:
Require Import Utf8.
Require Import Reals.
Require Import SetoidDec.
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Uti... | intro Habs. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Lemma obs_non_empty : forall config pt, obs_from_config config pt =/= @empty location _ _ _.
<Previous context>:
Require Import Utf8.
Require Import Reals.
Require Import SetoidDec.
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Uti... | pose (g := fin0 : G). |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Lemma obs_non_empty : forall config pt, obs_from_config config pt =/= @empty location _ _ _.
<Previous context>:
Require Import Utf8.
Require Import Reals.
Require Import SetoidDec.
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Uti... | specialize (Habs (config (Good g))). |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Lemma obs_non_empty : forall config pt, obs_from_config config pt =/= @empty location _ _ _.
<Previous context>:
Require Import Utf8.
Require Import Reals.
Require Import SetoidDec.
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Uti... | rewrite empty_spec in Habs. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Lemma obs_non_empty : forall config pt, obs_from_config config pt =/= @empty location _ _ _.
<Previous context>:
Require Import Utf8.
Require Import Reals.
Require Import SetoidDec.
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Uti... | assert (Hin := pos_in_config config origin (Good g)). |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Lemma obs_non_empty : forall config pt, obs_from_config config pt =/= @empty location _ _ _.
<Previous context>:
Require Import Utf8.
Require Import Reals.
Require Import SetoidDec.
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Uti... | simpl in Hin. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Lemma obs_non_empty : forall config pt, obs_from_config config pt =/= @empty location _ _ _.
<Previous context>:
Require Import Utf8.
Require Import Reals.
Require Import SetoidDec.
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Uti... | unfold id in Hin. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Lemma obs_non_empty : forall config pt, obs_from_config config pt =/= @empty location _ _ _.
<Previous context>:
Require Import Utf8.
Require Import Reals.
Require Import SetoidDec.
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Uti... | tauto. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Lemma obs_non_empty : forall config pt, obs_from_config config pt =/= @empty location _ _ _.
<Previous context>:
Require Import Utf8.
Require Import Reals.
Require Import SetoidDec.
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Uti... | Qed. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance contained_compat : Proper (equiv ==> Logic.eq ==> equiv ==> iff) contained.
<Previous context>:
Require Import Reals.
Require Import SetoidDec.
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Util.Bijection.
Require Import Pact... | Proof using . |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance contained_compat : Proper (equiv ==> Logic.eq ==> equiv ==> iff) contained.
<Previous context>:
Require Import SetoidDec.
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Util.Bijection.
Require Import Pactole.Util.Fin.
Require ... | intros ? ? Hc ? ? Hr ? ? Hconfig. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance contained_compat : Proper (equiv ==> Logic.eq ==> equiv ==> iff) contained.
<Previous context>:
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Util.Bijection.
Require Import Pactole.Util.Fin.
Require Import Pactole.Setting.
Re... | subst. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance contained_compat : Proper (equiv ==> Logic.eq ==> equiv ==> iff) contained.
<Previous context>:
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Util.Bijection.
Require Import Pactole.Util.Fin.
Require Import Pactole.Setting.
Re... | unfold contained. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance contained_compat : Proper (equiv ==> Logic.eq ==> equiv ==> iff) contained.
<Previous context>:
Require Import Lia.
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Util.Bijection.
Require Import Pactole.Util.Fin.
Require Import Pactole.Setting.
Re... | setoid_rewrite Hc. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance contained_compat : Proper (equiv ==> Logic.eq ==> equiv ==> iff) contained.
<Previous context>:
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Util.Bijection.
Require Import Pactole.Util.Fin.
Require Import Pactole.Setting.
Require Import Pactole... | setoid_rewrite Hconfig. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance contained_compat : Proper (equiv ==> Logic.eq ==> equiv ==> iff) contained.
<Previous context>:
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Util.Bijection.
Require Import Pactole.Util.Fin.
Require Import Pactole.Setting.
Require Import Pactole... | reflexivity. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance contained_compat : Proper (equiv ==> Logic.eq ==> equiv ==> iff) contained.
<Previous context>:
Require Import SetoidList.
Require Import Pactole.Util.Preliminary.
Require Import Pactole.Util.Bijection.
Require Import Pactole.Util.Fin.
Require Import Pactole.Setting.
Require Import Pactole... | Qed. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance imprisoned_compat : Proper (equiv ==> Logic.eq ==> @equiv _ Stream.stream_Setoid ==> iff) imprisoned.
<Previous context>:
Require Import Pactole.Util.Fin.
Require Import Pactole.Setting.
Require Import Pactole.Spaces.R2.
Require Import Pactole.Observations.SetObservation.
Require Import Pa... | Proof using . |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance imprisoned_compat : Proper (equiv ==> Logic.eq ==> @equiv _ Stream.stream_Setoid ==> iff) imprisoned.
<Previous context>:
Require Import Pactole.Setting.
Require Import Pactole.Spaces.R2.
Require Import Pactole.Observations.SetObservation.
Require Import Pactole.Models.Rigid.
Require Impor... | unfold imprisoned. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance imprisoned_compat : Proper (equiv ==> Logic.eq ==> @equiv _ Stream.stream_Setoid ==> iff) imprisoned.
<Previous context>:
Require Import Pactole.Spaces.R2.
Require Import Pactole.Observations.SetObservation.
Require Import Pactole.Models.Rigid.
Require Import Pactole.Models.NoByzantine.
Re... | repeat intro. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance imprisoned_compat : Proper (equiv ==> Logic.eq ==> @equiv _ Stream.stream_Setoid ==> iff) imprisoned.
<Previous context>:
Require Import Pactole.Spaces.R2.
Require Import Pactole.Observations.SetObservation.
Require Import Pactole.Models.Rigid.
Require Import Pactole.Models.NoByzantine.
Re... | apply Stream.forever_compat; trivial; []. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance imprisoned_compat : Proper (equiv ==> Logic.eq ==> @equiv _ Stream.stream_Setoid ==> iff) imprisoned.
<Previous context>:
Require Import Pactole.Observations.SetObservation.
Require Import Pactole.Models.Rigid.
Require Import Pactole.Models.NoByzantine.
Require Import Pactole.Models.Simila... | repeat intro. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance imprisoned_compat : Proper (equiv ==> Logic.eq ==> @equiv _ Stream.stream_Setoid ==> iff) imprisoned.
<Previous context>:
Require Import Pactole.Observations.SetObservation.
Require Import Pactole.Models.Rigid.
Require Import Pactole.Models.NoByzantine.
Require Import Pactole.Models.Simila... | apply Stream.instant_compat; trivial; []. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance imprisoned_compat : Proper (equiv ==> Logic.eq ==> @equiv _ Stream.stream_Setoid ==> iff) imprisoned.
<Previous context>:
Require Import Pactole.Models.Rigid.
Require Import Pactole.Models.NoByzantine.
Require Import Pactole.Models.Similarity.
Set Implicit Arguments.
Close Scope R_scope.
I... | now apply contained_compat. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance imprisoned_compat : Proper (equiv ==> Logic.eq ==> @equiv _ Stream.stream_Setoid ==> iff) imprisoned.
<Previous context>:
Require Import Pactole.Models.NoByzantine.
Require Import Pactole.Models.Similarity.
Set Implicit Arguments.
Close Scope R_scope.
Import Datatypes.
Import List.
Import ... | Qed. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance attracted_compat : Proper (equiv ==> eq ==> @equiv _ Stream.stream_Setoid ==> iff) attracted.
<Previous context>:
Close Scope R_scope.
Import Datatypes.
Import List.
Import SetoidClass.
Typeclasses eauto := (bfs).
Section ConvergenceAlgo.
(** There are [ub] good robots and no byzantine o... | Proof using . |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance attracted_compat : Proper (equiv ==> eq ==> @equiv _ Stream.stream_Setoid ==> iff) attracted.
<Previous context>:
Import Datatypes.
Import List.
Import SetoidClass.
Typeclasses eauto := (bfs).
Section ConvergenceAlgo.
(** There are [ub] good robots and no byzantine one. *)
Context {k : n... | intros ? ? Heq ? ? ?. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance attracted_compat : Proper (equiv ==> eq ==> @equiv _ Stream.stream_Setoid ==> iff) attracted.
<Previous context>:
Import Datatypes.
Import List.
Import SetoidClass.
Typeclasses eauto := (bfs).
Section ConvergenceAlgo.
(** There are [ub] good robots and no byzantine one. *)
Context {k : n... | now apply Stream.eventually_compat, imprisoned_compat. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance attracted_compat : Proper (equiv ==> eq ==> @equiv _ Stream.stream_Setoid ==> iff) attracted.
<Previous context>:
Import Datatypes.
Import List.
Import SetoidClass.
Typeclasses eauto := (bfs).
Section ConvergenceAlgo.
(** There are [ub] good robots and no byzantine one. *)
Context {k : n... | Qed. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Lemma synchro : ∀ r, solution_SSYNC r → solution_FSYNC r.
<Previous context>:
Proof using . now split. Qed.
(* BUG?: To help finding correct instances, loops otherwise! *)
Instance Loc : Location := {| location := R2 |}.
Instance Loc_VS : RealVectorSpace location := R2_VS.
Instance Loc_ES : Euclid... | Proof using . |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Lemma synchro : ∀ r, solution_SSYNC r → solution_FSYNC r.
<Previous context>:
(* BUG?: To help finding correct instances, loops otherwise! *)
Instance Loc : Location := {| location := R2 |}.
Instance Loc_VS : RealVectorSpace location := R2_VS.
Instance Loc_ES : EuclideanSpace location := R2_ES.
Re... | unfold solution_SSYNC. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Lemma synchro : ∀ r, solution_SSYNC r → solution_FSYNC r.
<Previous context>:
(* BUG?: To help finding correct instances, loops otherwise! *)
Instance Loc : Location := {| location := R2 |}.
Instance Loc_VS : RealVectorSpace location := R2_VS.
Instance Loc_ES : EuclideanSpace location := R2_ES.
Rem... | intros r Hfair config d Hd. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Lemma synchro : ∀ r, solution_SSYNC r → solution_FSYNC r.
<Previous context>:
(* BUG?: To help finding correct instances, loops otherwise! *)
Instance Loc : Location := {| location := R2 |}.
Instance Loc_VS : RealVectorSpace location := R2_VS.
Instance Loc_ES : EuclideanSpace location := R2_ES.
Rem... | apply Hfair, FSYNC_implies_Fair; autoclass. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Lemma synchro : ∀ r, solution_SSYNC r → solution_FSYNC r.
<Previous context>:
Instance Loc : Location := {| location := R2 |}.
Instance Loc_VS : RealVectorSpace location := R2_VS.
Instance Loc_ES : EuclideanSpace location := R2_ES.
Remove Hints R2_Setoid R2_EqDec : typeclass_instances.
Instance Inf... | Qed. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance convergeR2_pgm_compat : Proper (equiv ==> equiv) convergeR2_pgm.
<Previous context>:
Instance UpdateFun : update_function location (Similarity.similarity location) unit := {
update := fun _ _ _ pt _ => pt;
update_compat := ltac:(repeat intro; subst; auto) }.
Instance InactiveFun : ina... | Proof using . |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance convergeR2_pgm_compat : Proper (equiv ==> equiv) convergeR2_pgm.
<Previous context>:
update := fun _ _ _ pt _ => pt;
update_compat := ltac:(repeat intro; subst; auto) }.
Instance InactiveFun : inactive_function unit := {
inactive := fun config id _ => config id;
inactive_compat :=... | intros ? ? Heq. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance convergeR2_pgm_compat : Proper (equiv ==> equiv) convergeR2_pgm.
<Previous context>:
update := fun _ _ _ pt _ => pt;
update_compat := ltac:(repeat intro; subst; auto) }.
Instance InactiveFun : inactive_function unit := {
inactive := fun config id _ => config id;
inactive_compat :=... | unfold convergeR2_pgm. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance convergeR2_pgm_compat : Proper (equiv ==> equiv) convergeR2_pgm.
<Previous context>:
update := fun _ _ _ pt _ => pt;
update_compat := ltac:(repeat intro; subst; auto) }.
Instance InactiveFun : inactive_function unit := {
inactive := fun config id _ => config id;
inactive_compat :=... | apply isobarycenter_compat. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance convergeR2_pgm_compat : Proper (equiv ==> equiv) convergeR2_pgm.
<Previous context>:
update := fun _ _ _ pt _ => pt;
update_compat := ltac:(repeat intro; subst; auto) }.
Instance InactiveFun : inactive_function unit := {
inactive := fun config id _ => config id;
inactive_compat :=... | now rewrite Heq. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Instance convergeR2_pgm_compat : Proper (equiv ==> equiv) convergeR2_pgm.
<Previous context>:
update := fun _ _ _ pt _ => pt;
update_compat := ltac:(repeat intro; subst; auto) }.
Instance InactiveFun : inactive_function unit := {
inactive := fun config id _ => config id;
inactive_compat :=... | Qed. |
You are a Coq proof assistant. Given the current context, theorem statement, hypotheses and goal, suggest the next correct proof step in Coq. | <Theorem statement>: Theorem round_simplify : forall da config, SSYNC_da da -> round convergeR2 da config == fun id => if da.(activate) id then isobarycenter (@elements location _ _ _ (!! config)) else config id.
<Previous context>:
(* Refolding typeclass instances *)
Ltac changeR2 :=
change R2 with location in *;
... | Proof using ltc_0_k. |
End of preview. Expand in Data Studio
No dataset card yet
- Downloads last month
- 6