Datasets:

phanerozoic
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Coq-Verdi

statement stringlengths 1 1.48k	proof stringlengths 0 8.54k	type stringclasses 15 values	symbolic_name stringlengths 1 85	library stringclasses 3 values	filename stringclasses 31 values	imports listlengths 1 14	deps listlengths 0 38	docstring stringclasses 17 values	source_url stringclasses 1 value	commit stringclasses 1 value
A_eq_dec : forall x y : A, {x = y} + {x <> y}.		Hypothesis	A_eq_dec	Core	theories/Core/DupDropReordering.v	[ "Coq", "List", "Relations", "Permutation", "StructTact", "StructTactics", "Verdi", "Net", "ListNotations" ]	[]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
dup_drop_step : list A -> list A -> Prop	:= \| DDS_dup : forall l p, In p l -> dup_drop_step l (p :: l) \| DDS_drop : forall xs p ys, dup_drop_step (xs ++ p :: ys) (xs ++ ys).	Inductive	dup_drop_step	Core	theories/Core/DupDropReordering.v	[ "Coq", "List", "Relations", "Permutation", "StructTact", "StructTactics", "Verdi", "Net", "ListNotations" ]	[]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
dup_drop_step_star	:= clos_refl_trans_n1 _ dup_drop_step.	Definition	dup_drop_step_star	Core	theories/Core/DupDropReordering.v	[ "Coq", "List", "Relations", "Permutation", "StructTact", "StructTactics", "Verdi", "Net", "ListNotations" ]	[ "dup_drop_step" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
dup_drop_step_star_trans : forall l l' l'', dup_drop_step_star l l' -> dup_drop_step_star l' l'' -> dup_drop_step_star l l''.	Proof using. intros. apply clos_rt_rtn1_iff. eapply rt_trans; apply clos_rt_rtn1_iff; eauto. Qed.	Lemma	dup_drop_step_star_trans	Core	theories/Core/DupDropReordering.v	[ "Coq", "List", "Relations", "Permutation", "StructTact", "StructTactics", "Verdi", "Net", "ListNotations" ]	[ "dup_drop_step_star" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
dup_drop_step_star_step_n1 : forall l l' l'', dup_drop_step_star l l' -> dup_drop_step l' l'' -> dup_drop_step_star l l''.	Proof using. intros. econstructor; eauto. Qed.	Lemma	dup_drop_step_star_step_n1	Core	theories/Core/DupDropReordering.v	[ "Coq", "List", "Relations", "Permutation", "StructTact", "StructTactics", "Verdi", "Net", "ListNotations" ]	[ "dup_drop_step", "dup_drop_step_star" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
dup_drop_step_star_step_1n : forall l l' l'', dup_drop_step l l' -> dup_drop_step_star l' l'' -> dup_drop_step_star l l''.	Proof using. intros. apply clos_rt_rtn1_iff. apply clos_rt_rt1n_iff. econstructor; [eauto\|]. apply clos_rt_rt1n_iff. apply clos_rt_rtn1_iff. auto. Qed.	Lemma	dup_drop_step_star_step_1n	Core	theories/Core/DupDropReordering.v	[ "Coq", "List", "Relations", "Permutation", "StructTact", "StructTactics", "Verdi", "Net", "ListNotations" ]	[ "dup_drop_step", "dup_drop_step_star" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
dup_drop_step_star_step_1 : forall l l', dup_drop_step l l' -> dup_drop_step_star l l'.	Proof using. intros. eapply dup_drop_step_star_step_1n; eauto. constructor. Qed.	Lemma	dup_drop_step_star_step_1	Core	theories/Core/DupDropReordering.v	[ "Coq", "List", "Relations", "Permutation", "StructTact", "StructTactics", "Verdi", "Net", "ListNotations" ]	[ "dup_drop_step", "dup_drop_step_star", "dup_drop_step_star_step_1n" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
dup_drop_swap : forall l x y, dup_drop_step_star (x :: y :: l) (y :: x :: l).	Proof using. intros. eapply dup_drop_step_star_step_1n; [eapply DDS_dup with (p := y); simpl; auto\|]. eapply dup_drop_step_star_step_1n. eapply DDS_drop with (xs := [y; x]) (p := y) (ys := l). constructor. Qed.	Lemma	dup_drop_swap	Core	theories/Core/DupDropReordering.v	[ "Coq", "List", "Relations", "Permutation", "StructTact", "StructTactics", "Verdi", "Net", "ListNotations" ]	[ "dup_drop_step_star", "dup_drop_step_star_step_1n" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
dup_drop_cons : forall l l' x, dup_drop_step_star l l' -> dup_drop_step_star (x :: l) (x :: l').	Proof using. induction 1. - constructor. - invc H. + eapply dup_drop_step_star_trans; [eauto\|]. eapply dup_drop_step_star_step_1n; [eapply DDS_dup with (p := p); simpl; auto\|]. auto using dup_drop_swap. + eapply dup_drop_step_star_trans; [eauto\|]. eapply dup_drop_step_sta...	Lemma	dup_drop_cons	Core	theories/Core/DupDropReordering.v	[ "Coq", "List", "Relations", "Permutation", "StructTact", "StructTactics", "Verdi", "Net", "ListNotations" ]	[ "dup_drop_step_star", "dup_drop_step_star_step_1n", "dup_drop_step_star_trans", "dup_drop_swap" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
dup_drop_Permutation : forall l l', Permutation l l' -> dup_drop_step_star l l'.	Proof using. induction 1. - constructor. - auto using dup_drop_cons. - auto using dup_drop_swap. - eauto using dup_drop_step_star_trans. Qed.	Lemma	dup_drop_Permutation	Core	theories/Core/DupDropReordering.v	[ "Coq", "List", "Relations", "Permutation", "StructTact", "StructTactics", "Verdi", "Net", "ListNotations" ]	[ "dup_drop_cons", "dup_drop_step_star", "dup_drop_step_star_trans", "dup_drop_swap" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
remove_not_in_nop : forall a l, ~ In a l -> remove A_eq_dec a l = l.	Proof using. induction l; simpl; intuition. break_if; congruence. Qed.	Lemma	remove_not_in_nop	Core	theories/Core/DupDropReordering.v	[ "Coq", "List", "Relations", "Permutation", "StructTact", "StructTactics", "Verdi", "Net", "ListNotations" ]	[ "A_eq_dec", "remove" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
dup_drop_in : forall l l' a, dup_drop_step_star l l' -> In a l' -> In a l.	Proof using. induction 1; intros. - auto. - invc H. + simpl in *. intuition. subst. auto. + apply IHclos_refl_trans_n1. find_apply_lem_hyp in_app_or. intuition auto with datatypes. Qed.	Lemma	dup_drop_in	Core	theories/Core/DupDropReordering.v	[ "Coq", "List", "Relations", "Permutation", "StructTact", "StructTactics", "Verdi", "Net", "ListNotations" ]	[ "dup_drop_step_star" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
dup_drop_dup_early : forall l l' a, dup_drop_step_star l l' -> In a l -> dup_drop_step_star l (a :: l').	Proof using. induction 1; intros. - apply dup_drop_step_star_step_1. constructor. auto. - concludes. eapply dup_drop_step_star_trans; eauto. apply dup_drop_cons. apply dup_drop_step_star_step_1. auto. Qed.	Lemma	dup_drop_dup_early	Core	theories/Core/DupDropReordering.v	[ "Coq", "List", "Relations", "Permutation", "StructTact", "StructTactics", "Verdi", "Net", "ListNotations" ]	[ "dup_drop_cons", "dup_drop_step_star", "dup_drop_step_star_step_1", "dup_drop_step_star_trans" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
dup_drop_step_star_remove_In : forall l' l a, In a l' -> dup_drop_step_star l (remove A_eq_dec a l') -> dup_drop_step_star (a :: l) l'.	Proof using. induction l'; simpl; intuition. - subst. break_if; try congruence. destruct (in_dec A_eq_dec a0 l'). + find_apply_hyp_hyp. eapply dup_drop_step_star_trans; eauto. eapply dup_drop_step_star_step_1. apply DDS_dup; auto. + rewrite remove_not_in_nop in * by aut...	Lemma	dup_drop_step_star_remove_In	Core	theories/Core/DupDropReordering.v	[ "Coq", "List", "Relations", "Permutation", "StructTact", "StructTactics", "Verdi", "Net", "ListNotations" ]	[ "A_eq_dec", "dup_drop_cons", "dup_drop_dup_early", "dup_drop_in", "dup_drop_step_star", "dup_drop_step_star_step_1", "dup_drop_step_star_step_n1", "dup_drop_step_star_trans", "remove", "remove_not_in_nop" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
remove_In_elim : forall x a l, In x (remove A_eq_dec a l) -> x <> a /\ In x l.	Proof using. induction l; simpl; intuition; break_if; subst; simpl in *; intuition. Qed.	Lemma	remove_In_elim	Core	theories/Core/DupDropReordering.v	[ "Coq", "List", "Relations", "Permutation", "StructTact", "StructTactics", "Verdi", "Net", "ListNotations" ]	[ "A_eq_dec", "remove" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
dup_drop_reorder : forall l l' : list A, (forall x, In x l' -> In x l) -> dup_drop_step_star l l'.	Proof using A_eq_dec. induction l; intros. - destruct l'. + constructor. + simpl in *. exfalso. eauto. - destruct (in_dec A_eq_dec a l'). + eapply dup_drop_step_star_remove_In. auto. apply IHl. intros. find_apply_lem_hyp remove_In_elim. intuition. fi...	Lemma	dup_drop_reorder	Core	theories/Core/DupDropReordering.v	[ "Coq", "List", "Relations", "Permutation", "StructTact", "StructTactics", "Verdi", "Net", "ListNotations" ]	[ "A_eq_dec", "dup_drop_step_star", "dup_drop_step_star_remove_In", "dup_drop_step_star_step_1n", "remove_In_elim" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
step_failure_dup_drop_step : forall ps ps' Sigma f, dup_drop_step_star _ ps ps' -> step_failure_star (f, mkNetwork ps Sigma) (f, mkNetwork ps' Sigma) [].	Proof using. induction 1. - constructor. - match goal with \| [ H : dup_drop_step _ _ _ \|- _ ] => invc H end. + find_apply_lem_hyp in_split. break_exists. break_and. subst. apply refl_trans_n1_1n_trace. eapply RTn1TStep with (cs := []). * apply refl_trans_1n_n1_trace...	Theorem	step_failure_dup_drop_step	Core	theories/Core/DupDropReordering.v	[ "Coq", "List", "Relations", "Permutation", "StructTact", "StructTactics", "Verdi", "Net", "ListNotations" ]	[ "dup_drop_step", "dup_drop_step_star", "refl_trans_1n_n1_trace", "refl_trans_n1_1n_trace", "step_failure_star" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
ordered_dynamic_uninitialized_state : forall net failed tr, step_ordered_dynamic_failure_star step_ordered_dynamic_failure_init (failed, net) tr -> forall n, ~ In n (odnwNodes net) -> odnwState net n = None.	Proof using. move => net failed tr H. remember step_ordered_dynamic_failure_init as y in *. have ->: net = snd (failed, net) by []. move: Heqy. induction H using refl_trans_1n_trace_n1_ind => H_init /=; first by rewrite H_init. concludes => {H_init}. match goal with \| [ H : step_ordered_dynamic_failure _ _ _ \|- _ ] => ...	Lemma	ordered_dynamic_uninitialized_state	Core	theories/Core/DynamicNetLemmas.v	[ "Verdi", "StructTact", "Update", "Coq", "FunctionalExtensionality", "Sumbool", "Relation_Definitions", "RelationClasses", "Ssrexport" ]	[ "name_eq_dec", "refl_trans_1n_trace_n1_ind", "step_ordered_dynamic_failure", "step_ordered_dynamic_failure_init", "step_ordered_dynamic_failure_star" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
ordered_dynamic_initialized_state : forall net failed tr, step_ordered_dynamic_failure_star step_ordered_dynamic_failure_init (failed, net) tr -> forall n, In n (odnwNodes net) -> exists d, odnwState net n = Some d.	Proof using. move => net failed tr H. remember step_ordered_dynamic_failure_init as y in *. have ->: net = snd (failed, net) by []. move: Heqy. induction H using refl_trans_1n_trace_n1_ind => H_init /=; first by rewrite H_init. repeat find_rewrite. concludes => {H_init}. match goal with \| [ H : step_ordered_dynamic_fai...	Lemma	ordered_dynamic_initialized_state	Core	theories/Core/DynamicNetLemmas.v	[ "Verdi", "StructTact", "Update", "Coq", "FunctionalExtensionality", "Sumbool", "Relation_Definitions", "RelationClasses", "Ssrexport" ]	[ "refl_trans_1n_trace_n1_ind", "step_ordered_dynamic_failure", "step_ordered_dynamic_failure_init", "step_ordered_dynamic_failure_star" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
ordered_dynamic_failed_then_initialized : forall net failed tr, step_ordered_dynamic_failure_star step_ordered_dynamic_failure_init (failed, net) tr -> forall n, In n failed -> In n (odnwNodes net).	Proof using. move => net failed tr H. remember step_ordered_dynamic_failure_init as y in *. have ->: failed = fst (failed, net) by []. have H_eq_o: net = snd (failed, net) by []. rewrite {2}H_eq_o {H_eq_o}. move: Heqy. induction H using refl_trans_1n_trace_n1_ind => H_init /=; first by rewrite H_init. repeat find_rewri...	Lemma	ordered_dynamic_failed_then_initialized	Core	theories/Core/DynamicNetLemmas.v	[ "Verdi", "StructTact", "Update", "Coq", "FunctionalExtensionality", "Sumbool", "Relation_Definitions", "RelationClasses", "Ssrexport" ]	[ "refl_trans_1n_trace_n1_ind", "step_ordered_dynamic_failure", "step_ordered_dynamic_failure_init", "step_ordered_dynamic_failure_star" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
ordered_dynamic_state_not_initialized_not_failed : forall net failed tr, step_ordered_dynamic_failure_star step_ordered_dynamic_failure_init (failed, net) tr -> forall n, ~ In n (odnwNodes net) -> ~ In n failed.	Proof using. move => net failed tr H. remember step_ordered_dynamic_failure_init as y in *. have ->: failed = fst (failed, net) by []. have H_eq_o: net = snd (failed, net) by []. rewrite {1}H_eq_o {H_eq_o}. move: Heqy. induction H using refl_trans_1n_trace_n1_ind => H_init /=; first by rewrite H_init. repeat find_rewri...	Lemma	ordered_dynamic_state_not_initialized_not_failed	Core	theories/Core/DynamicNetLemmas.v	[ "Verdi", "StructTact", "Update", "Coq", "FunctionalExtensionality", "Sumbool", "Relation_Definitions", "RelationClasses", "Ssrexport" ]	[ "refl_trans_1n_trace_n1_ind", "step_ordered_dynamic_failure", "step_ordered_dynamic_failure_init", "step_ordered_dynamic_failure_star" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
ordered_dynamic_no_outgoing_uninitialized : forall onet failed tr, step_ordered_dynamic_failure_star step_ordered_dynamic_failure_init (failed, onet) tr -> forall n, ~ In n (odnwNodes onet) -> forall n', onet.(odnwPackets) n n' = [].	Proof using. move => net failed tr H. remember step_ordered_dynamic_failure_init as y in *. have ->: net = snd (failed, net) by []. move: Heqy. induction H using refl_trans_1n_trace_n1_ind => H_init /=; first by rewrite H_init. concludes => {H_init}. match goal with \| [ H : step_ordered_dynamic_failure _ _ _ \|- _ ] => ...	Lemma	ordered_dynamic_no_outgoing_uninitialized	Core	theories/Core/DynamicNetLemmas.v	[ "Verdi", "StructTact", "Update", "Coq", "FunctionalExtensionality", "Sumbool", "Relation_Definitions", "RelationClasses", "Ssrexport" ]	[ "refl_trans_1n_trace_n1_ind", "step_ordered_dynamic_failure", "step_ordered_dynamic_failure_init", "step_ordered_dynamic_failure_star" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
ordered_dynamic_nodes_no_dup : forall onet failed tr, step_ordered_dynamic_failure_star step_ordered_dynamic_failure_init (failed, onet) tr -> NoDup (odnwNodes onet).	Proof using. move => net failed tr H. remember step_ordered_dynamic_failure_init as y in *. have ->: net = snd (failed, net) by []. move: Heqy. induction H using refl_trans_1n_trace_n1_ind => H_init. rewrite H_init /=. exact: NoDup_nil. concludes => {H_init}. match goal with \| [ H : step_ordered_dynamic_failure _ _...	Lemma	ordered_dynamic_nodes_no_dup	Core	theories/Core/DynamicNetLemmas.v	[ "Verdi", "StructTact", "Update", "Coq", "FunctionalExtensionality", "Sumbool", "Relation_Definitions", "RelationClasses", "Ssrexport" ]	[ "refl_trans_1n_trace_n1_ind", "step_ordered_dynamic_failure", "step_ordered_dynamic_failure_init", "step_ordered_dynamic_failure_star" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
GhostMultiParams `(P : MultiParams)	:= { ghost_data : Type; ghost_init : ghost_data ; ghost_net_handlers : name -> name -> msg -> (ghost_data * data) -> ghost_data; ghost_input_handlers : name -> input -> (ghost_data * data) -> ghost_data }.	Class	GhostMultiParams	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "MultiParams", "data", "input", "msg", "name" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
refined_net_handlers me src m st	:= let '(out, st', ps) := net_handlers me src m (snd st) in (out, (ghost_net_handlers me src m st, st'), ps).	Definition	refined_net_handlers	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "src" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
refined_input_handlers me inp st	:= let '(out, st', ps) := input_handlers me inp (snd st) in (out, (ghost_input_handlers me inp st, st'), ps).	Definition	refined_input_handlers	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
refined_init_handlers (n : name) : ghost_data * data	:= (ghost_init, init_handlers n).	Definition	refined_init_handlers	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "data", "name" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
refined_reboot (st : ghost_data * data)	:= (fst st , reboot (snd st)).	Definition	refined_reboot	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "data" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
refined_base_params : BaseParams	:= { data := (ghost_data * data)%type ; input := input ; output := output }.	Instance	refined_base_params	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "BaseParams", "data", "input", "output" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
refined_multi_params : MultiParams _	:= { name := name ; msg := msg ; msg_eq_dec := msg_eq_dec ; name_eq_dec := name_eq_dec ; nodes := nodes ; all_names_nodes := all_names_nodes ; no_dup_nodes := no_dup_nodes ; init_handlers := refined_init_handlers; net_handlers := refined_net_handlers ; input_handlers := refined...	Instance	refined_multi_params	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "MultiParams", "all_names_nodes", "msg", "msg_eq_dec", "name", "name_eq_dec", "no_dup_nodes", "nodes", "refined_init_handlers", "refined_input_handlers", "refined_net_handlers" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
refined_failure_params : FailureParams _	:= { reboot := refined_reboot }.	Instance	refined_failure_params	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "FailureParams", "refined_reboot" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
deghost_packet p	:= @mkPacket _ multi_params (@pSrc _ refined_multi_params p) (pDst p) (pBody p).	Definition	deghost_packet	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "multi_params", "refined_multi_params" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
deghost (net : @network _ refined_multi_params) : (@network _ multi_params).	refine (@mkNetwork _ multi_params (map deghost_packet (nwPackets net)) _ ). intros. destruct net as [? nwState]. concludes. destruct nwState. auto. Defined.	Definition	deghost	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "deghost_packet", "multi_params", "network", "refined_multi_params" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
deghost_prop I (failed_net : list name * network) : Prop	:= I ((fst failed_net), deghost (snd failed_net)).	Definition	deghost_prop	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "deghost", "name", "network" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
refined_base_params_tot_map : BaseParamsTotalMap refined_base_params base_params	:= { tot_map_data := snd ; tot_map_input := id ; tot_map_output := id }.	Instance	refined_base_params_tot_map	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "BaseParamsTotalMap", "base_params", "refined_base_params" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
refined_multi_params_name_tot_map : MultiParamsNameTotalMap refined_multi_params multi_params	:= { tot_map_name := id ; tot_map_name_inv := id }.	Instance	refined_multi_params_name_tot_map	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "MultiParamsNameTotalMap", "multi_params", "refined_multi_params" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
refined_multi_params_name_tot_map_bijective : MultiParamsNameTotalMapBijective refined_multi_params_name_tot_map	:= { tot_map_name_inv_inverse := fun _ => eq_refl ; tot_map_name_inverse_inv := fun _ => eq_refl }.	Instance	refined_multi_params_name_tot_map_bijective	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "MultiParamsNameTotalMapBijective", "eq_refl", "refined_multi_params_name_tot_map" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
refined_multi_params_tot_msg_map : MultiParamsMsgTotalMap refined_multi_params multi_params	:= { tot_map_msg := id }.	Instance	refined_multi_params_tot_msg_map	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "MultiParamsMsgTotalMap", "multi_params", "refined_multi_params" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
refined_multi_params_map_congruency : MultiParamsTotalMapCongruency refined_base_params_tot_map refined_multi_params_name_tot_map refined_multi_params_tot_msg_map := { tot_init_handlers_eq := fun _ => eq_refl ; tot_net_handlers_eq := _ ; tot_input_handlers_eq := _ }.	Next Obligation. rewrite /tot_mapped_net_handlers /= /refined_net_handlers /= /tot_map_name_msgs /= /id /=. repeat break_let. find_inversion. by rewrite /= -/id map_id map_fst_snd_id. Qed.	Instance	refined_multi_params_map_congruency	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "MultiParamsTotalMapCongruency", "eq_refl", "map_id", "refined_base_params_tot_map", "refined_multi_params_name_tot_map", "refined_multi_params_tot_msg_map", "refined_net_handlers", "tot_map_name_msgs", "tot_mapped_net_handlers" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
refined_failure_params_map_congruency : FailureParamsTotalMapCongruency refined_failure_params failure_params refined_base_params_tot_map	:= { tot_reboot_eq := fun _ => eq_refl }.	Instance	refined_failure_params_map_congruency	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "FailureParamsTotalMapCongruency", "eq_refl", "refined_base_params_tot_map", "refined_failure_params" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
map_id_tr : forall out, map (fun e : name * (input + list output) => let (n, s) := e in match s with \| inl io => (n, inl io) \| inr lo => (n, inr (map id lo)) end) out = out.	Proof using. elim => //. move => tr l IH. rewrite /= IH. break_let. break_match => //=. by rewrite map_id. Qed.	Lemma	map_id_tr	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "input", "map_id", "name", "output" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
ghost_simulation_1 : forall net net' failed failed' out, @step_failure _ _ refined_failure_params (failed, net) (failed', net') out -> @step_failure _ _ failure_params (failed, deghost net) (failed', deghost net') out.	Proof using. move => net net' failed failed' out H_step. apply step_failure_tot_mapped_simulation_1 in H_step. rewrite /tot_map_name /tot_map_net /= 2!map_id /id /= in H_step. rewrite /tot_map_trace_occ /= /id /= in H_step. rewrite /tot_map_packet /= /id /= in H_step. rewrite /deghost /=. rewrite -/id map_id_tr in H_st...	Theorem	ghost_simulation_1	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "deghost", "dst", "map_id", "map_id_tr", "packet", "refined_failure_params", "src", "step_failure", "step_failure_tot_mapped_simulation_1", "tot_map_net", "tot_map_packet", "tot_map_trace_occ" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
ghost_simulation_2 : forall net net' failed failed' out gnet, @step_failure _ _ failure_params (failed, net) (failed', net') out -> deghost gnet = net -> exists gnet', step_failure (failed, gnet) (failed', gnet') out /\ deghost gnet' = net'.	Proof using. move => net net' failed failed' out gnet H_step H_eq. eapply step_failure_tot_mapped_simulation_2 in H_step => //. - move: H_step => [gnet' [H_step H_eq_net]]. exists gnet'. split; eauto. rewrite -H_eq_net {H_eq_net H_step}. rewrite /deghost /tot_map_net /= /id /= /tot_map_packet /= /id /=. set n...	Theorem	ghost_simulation_2	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "deghost", "map_id", "packet", "step_failure", "step_failure_tot_mapped_simulation_2", "tot_map_net", "tot_map_packet" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
ghost_packet p	:= @mkPacket _ refined_multi_params (@pSrc _ multi_params p) (pDst p) (pBody p).	Definition	ghost_packet	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "multi_params", "refined_multi_params" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
reghost (net : @network _ multi_params) : @network _ refined_multi_params.	refine (@mkNetwork _ refined_multi_params (map ghost_packet (nwPackets net)) _ ). intros. destruct net as [? nwState]. concludes. exact (ghost_init, nwState). Defined.	Definition	reghost	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "ghost_packet", "multi_params", "network", "refined_multi_params" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
reghost_deghost_partial_inverses : forall net, deghost (reghost net) = net.	Proof using. destruct net. unfold deghost, reghost. simpl in *. f_equal. rewrite map_map. map_id. Qed.	Lemma	reghost_deghost_partial_inverses	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "deghost", "map_id", "reghost" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
ghost_invariant_lift : forall P : _ -> Prop, (forall net net' failed failed' out, @step_failure _ _ failure_params (failed, net) (failed', net') out -> P net -> P net') -> (forall net net' failed failed' out, step_failure (failed, net) (failed', net') out -> P (deghost net) ...	Proof using. intros. eauto using ghost_simulation_1. Qed.	Theorem	ghost_invariant_lift	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "deghost", "ghost_simulation_1", "step_failure" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
ghost_invariant_lower : forall P : _ -> Prop, (forall net net' failed failed' out, step_failure (failed, net) (failed', net') out -> P (deghost net) -> P (deghost net')) -> (forall net net' failed failed' out, @step_failure _ _ failure_params (failed, net) (failed', net') out -> ...	Proof using. intros. apply ghost_simulation_2 with (gnet := reghost net) in H0. - break_exists. intuition. subst. eapply H; eauto. rewrite reghost_deghost_partial_inverses. auto. - eauto using reghost_deghost_partial_inverses. Qed.	Theorem	ghost_invariant_lower	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "deghost", "ghost_simulation_2", "reghost", "reghost_deghost_partial_inverses", "step_failure" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
MsgGhostMultiParams `(P : MultiParams)	:= { ghost_msg : Type; ghost_msg_eq_dec : forall x y : ghost_msg, {x = y} + {x <> y} ; ghost_msg_default : ghost_msg ; write_ghost_msg : name -> data -> ghost_msg }.	Class	MsgGhostMultiParams	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "MultiParams", "data", "name" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
add_ghost_msg (me : name) (st : data) (ps : list (name * msg)) : list (name * (ghost_msg * msg))	:= map (fun m => (fst m, (write_ghost_msg me st, snd m))) ps.	Definition	add_ghost_msg	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "data", "msg", "name" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_refined_net_handlers me src (m : ghost_msg * msg) st	:= let '(out, st', ps) := net_handlers me src (snd m) st in (out, st', add_ghost_msg me st' ps).	Definition	mgv_refined_net_handlers	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "add_ghost_msg", "msg", "src" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_refined_input_handlers me inp st	:= let '(out, st', ps) := input_handlers me inp st in (out, st', add_ghost_msg me st' ps).	Definition	mgv_refined_input_handlers	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "add_ghost_msg" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_msg_eq_dec : forall x y : ghost_msg * msg, {x = y} + {x <> y}.	Proof using. intros. decide equality; auto using msg_eq_dec, ghost_msg_eq_dec. Qed.	Definition	mgv_msg_eq_dec	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "msg", "msg_eq_dec" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_refined_base_params : BaseParams	:= { data := data ; input := input ; output := output }.	Instance	mgv_refined_base_params	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "BaseParams", "data", "input", "output" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_refined_multi_params : MultiParams _	:= { name := name ; msg := (ghost_msg * msg) ; msg_eq_dec := mgv_msg_eq_dec ; name_eq_dec := name_eq_dec ; nodes := nodes ; all_names_nodes := all_names_nodes ; no_dup_nodes := no_dup_nodes ; init_handlers := init_handlers; net_handlers := mgv_refined_net_handlers ; input_handl...	Instance	mgv_refined_multi_params	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "MultiParams", "all_names_nodes", "mgv_msg_eq_dec", "mgv_refined_input_handlers", "mgv_refined_net_handlers", "msg", "msg_eq_dec", "name", "name_eq_dec", "no_dup_nodes", "nodes" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_refined_failure_params : FailureParams _	:= { reboot := (@reboot base_params multi_params failure_params) }.	Instance	mgv_refined_failure_params	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "FailureParams", "base_params", "multi_params" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_deghost_packet p	:= @mkPacket _ multi_params (@pSrc _ mgv_refined_multi_params p) (pDst p) (snd (pBody p)).	Definition	mgv_deghost_packet	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "mgv_refined_multi_params", "multi_params" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_deghost (net : @network _ mgv_refined_multi_params) : (@network _ multi_params).	refine (@mkNetwork _ multi_params (map mgv_deghost_packet (nwPackets net)) _ ). intros. destruct net. concludes. auto. Defined.	Definition	mgv_deghost	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "mgv_deghost_packet", "mgv_refined_multi_params", "multi_params", "network" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_refined_base_params_tot_map : BaseParamsTotalMap mgv_refined_base_params base_params	:= { tot_map_data := id ; tot_map_input := id ; tot_map_output := id }.	Instance	mgv_refined_base_params_tot_map	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "BaseParamsTotalMap", "base_params", "mgv_refined_base_params" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_refined_multi_params_name_tot_map : MultiParamsNameTotalMap mgv_refined_multi_params multi_params	:= { tot_map_name := id ; tot_map_name_inv := id ; }.	Instance	mgv_refined_multi_params_name_tot_map	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "MultiParamsNameTotalMap", "mgv_refined_multi_params", "multi_params" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_refined_multi_params_name_tot_map_bijective : MultiParamsNameTotalMapBijective mgv_refined_multi_params_name_tot_map	:= { tot_map_name_inv_inverse := fun _ => eq_refl ; tot_map_name_inverse_inv := fun _ => eq_refl }.	Instance	mgv_refined_multi_params_name_tot_map_bijective	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "MultiParamsNameTotalMapBijective", "eq_refl", "mgv_refined_multi_params_name_tot_map" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_refined_multi_params_tot_map : MultiParamsMsgTotalMap mgv_refined_multi_params multi_params	:= { tot_map_msg := snd ; }.	Instance	mgv_refined_multi_params_tot_map	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "MultiParamsMsgTotalMap", "mgv_refined_multi_params", "multi_params" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_refined_multi_params_map_congruency : MultiParamsTotalMapCongruency mgv_refined_base_params_tot_map mgv_refined_multi_params_name_tot_map mgv_refined_multi_params_tot_map := { tot_init_handlers_eq := fun _ => eq_refl ; tot_net_handlers_eq := _ ; tot_input_handlers_eq := _ }.	Next Obligation. rewrite /tot_mapped_net_handlers /= /mgv_refined_net_handlers /= /tot_map_name_msgs /= /id /=. repeat break_let. find_inversion. rewrite -/id map_id /= /add_ghost_msg /=. elim l0 => //=. case => n m' l IH. find_inversion. by find_rewrite; find_rewrite. Qed.	Instance	mgv_refined_multi_params_map_congruency	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "MultiParamsTotalMapCongruency", "add_ghost_msg", "eq_refl", "map_id", "mgv_refined_base_params_tot_map", "mgv_refined_multi_params_name_tot_map", "mgv_refined_multi_params_tot_map", "mgv_refined_net_handlers", "tot_map_name_msgs", "tot_mapped_net_handlers" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_refined_failure_params_map_congruency : FailureParamsTotalMapCongruency mgv_refined_failure_params failure_params mgv_refined_base_params_tot_map	:= { tot_reboot_eq := fun _ => eq_refl }.	Instance	mgv_refined_failure_params_map_congruency	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "FailureParamsTotalMapCongruency", "eq_refl", "mgv_refined_base_params_tot_map", "mgv_refined_failure_params" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_map_id_tr : forall out, map (fun e : name * (input + list output) => let (n, s) := e in match s with \| inl io => (n, inl io) \| inr lo => (n, inr (map id lo)) end) out = out.	Proof using. elim => //. move => tr l IH. rewrite /= IH. break_let. break_match => //. by rewrite map_id. Qed.	Lemma	mgv_map_id_tr	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "input", "map_id", "name", "output" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_ghost_simulation_1 : forall net net' failed failed' out, @step_failure _ _ mgv_refined_failure_params (failed, net) (failed', net') out -> @step_failure _ _ failure_params (failed, mgv_deghost net) (failed', mgv_deghost net') out.	Proof using. move => net net' failed failed' out H_step. apply step_failure_tot_mapped_simulation_1 in H_step. rewrite /tot_map_name /tot_map_net /= 2!map_id /id /= in H_step. rewrite /tot_map_trace_occ /= /id /= in H_step. rewrite /tot_map_packet /= /id /= in H_step. rewrite /mgv_deghost /=. rewrite -/id mgv_map_id_tr...	Theorem	mgv_ghost_simulation_1	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "dst", "map_id", "mgv_deghost", "mgv_map_id_tr", "mgv_refined_failure_params", "packet", "src", "step_failure", "step_failure_tot_mapped_simulation_1", "tot_map_net", "tot_map_packet", "tot_map_trace_occ" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_ghost_packet p	:= @mkPacket _ mgv_refined_multi_params (@pSrc _ multi_params p) (pDst p) (ghost_msg_default, pBody p).	Definition	mgv_ghost_packet	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "mgv_refined_multi_params", "multi_params" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_reghost (net : @network _ multi_params) : @network _ mgv_refined_multi_params.	refine (@mkNetwork _ mgv_refined_multi_params (map mgv_ghost_packet (nwPackets net)) _ ). intros. destruct net. concludes. auto. Defined.	Definition	mgv_reghost	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "mgv_ghost_packet", "mgv_refined_multi_params", "multi_params", "network" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_reghost_deghost_partial_inverses : forall net, mgv_deghost (mgv_reghost net) = net.	Proof using. destruct net. unfold mgv_deghost, mgv_reghost. simpl in *. f_equal. rewrite map_map. map_id. Qed.	Lemma	mgv_reghost_deghost_partial_inverses	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "map_id", "mgv_deghost", "mgv_reghost" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_ghost_simulation_2 : forall net net' failed failed' out gnet, @step_failure _ _ failure_params (failed, net) (failed', net') out -> mgv_deghost gnet = net -> exists gnet', step_failure (failed, gnet) (failed', gnet') out /\ mgv_deghost gnet' = net'.	Proof using. move => net net' failed failed' out gnet H_step H_eq. eapply step_failure_tot_mapped_simulation_2 in H_step => //. - move: H_step => [gnet' [H_step H_eq_net]]. exists gnet'. split; eauto. rewrite -H_eq_net {H_step H_eq_net}. rewrite /mgv_deghost /tot_map_net /= /id /= /tot_map_packet /= /id /=. s...	Theorem	mgv_ghost_simulation_2	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "map_id", "mgv_deghost", "packet", "step_failure", "step_failure_tot_mapped_simulation_2", "tot_map_net", "tot_map_packet" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_ghost_invariant_lift : forall P : _ -> Prop, (forall net net' failed failed' out, @step_failure _ _ failure_params (failed, net) (failed', net') out -> P net -> P net') -> (forall net net' failed failed' out, step_failure (failed, net) (failed', net') out -> P (mgv_degho...	Proof using. intros. eauto using mgv_ghost_simulation_1. Qed.	Theorem	mgv_ghost_invariant_lift	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "mgv_deghost", "mgv_ghost_simulation_1", "step_failure" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
mgv_ghost_invariant_lower : forall P : _ -> Prop, (forall net net' failed failed' out, step_failure (failed, net) (failed', net') out -> P (mgv_deghost net) -> P (mgv_deghost net')) -> (forall net net' failed failed' out, @step_failure _ _ failure_params (failed, net) (failed', net...	Proof using. intros. apply mgv_ghost_simulation_2 with (gnet := mgv_reghost net) in H0. - break_exists. intuition. subst. eapply H; eauto. rewrite mgv_reghost_deghost_partial_inverses. auto. - eauto using mgv_reghost_deghost_partial_inverses. Qed.	Theorem	mgv_ghost_invariant_lower	Core	theories/Core/GhostSimulations.v	[ "Coq", "List", "StructTact", "StructTactics", "Util", "Verdi", "Net", "TotalMapSimulations", "FunctionalExtensionality", "Ssrexport" ]	[ "mgv_deghost", "mgv_ghost_simulation_2", "mgv_reghost", "mgv_reghost_deghost_partial_inverses", "step_failure" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
GenHandler (W S O A : Type) : Type	:= S -> A * list O * S * list W % type.	Definition	GenHandler	Core	theories/Core/HandlerMonad.v	[ "Coq", "List", "ListNotations" ]	[]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
ret {W S O A : Type} (a : A) : GenHandler W S O A	:= fun s => (a, [], s, []).	Definition	ret	Core	theories/Core/HandlerMonad.v	[ "Coq", "List", "ListNotations" ]	[ "GenHandler" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
bind {W S O A B : Type} (m : GenHandler W S O A) (f : A -> GenHandler W S O B) : GenHandler W S O B	:= fun s => let '(a, os1, s', ws1) := m s in let '(b, os2, s'', ws2) := f a s' in (b, os1 ++ os2, s'', ws1 ++ ws2).	Definition	bind	Core	theories/Core/HandlerMonad.v	[ "Coq", "List", "ListNotations" ]	[ "GenHandler" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
send {W S O} (w : W) : GenHandler W S O unit	:= fun s => (tt, [], s, [w]).	Definition	send	Core	theories/Core/HandlerMonad.v	[ "Coq", "List", "ListNotations" ]	[ "GenHandler" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
write_output {W S O} (o : O) : GenHandler W S O unit	:= fun s => (tt, [o], s, []).	Definition	write_output	Core	theories/Core/HandlerMonad.v	[ "Coq", "List", "ListNotations" ]	[ "GenHandler" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
modify {W S O} (f : S -> S) : GenHandler W S O unit	:= fun s => (tt, [], f s, []).	Definition	modify	Core	theories/Core/HandlerMonad.v	[ "Coq", "List", "ListNotations" ]	[ "GenHandler" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
put {W S O} (s : S) : GenHandler W S O unit	:= fun _ => (tt, [], s, []).	Definition	put	Core	theories/Core/HandlerMonad.v	[ "Coq", "List", "ListNotations" ]	[ "GenHandler" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
get {W S O} : GenHandler W S O S	:= fun s => (s, [], s, []).	Definition	get	Core	theories/Core/HandlerMonad.v	[ "Coq", "List", "ListNotations" ]	[ "GenHandler" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
runGenHandler {W S O A} (s : S) (h : GenHandler W S O A) : A * list O * S * list W % type	:= h s.	Definition	runGenHandler	Core	theories/Core/HandlerMonad.v	[ "Coq", "List", "ListNotations" ]	[ "GenHandler" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
runGenHandler_ignore {W S O A} (s : S) (h : GenHandler W S O A) : list O * S * list W % type	:= let '(_, os, s', ms) := h s in (os, s', ms).	Definition	runGenHandler_ignore	Core	theories/Core/HandlerMonad.v	[ "Coq", "List", "ListNotations" ]	[ "GenHandler" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
runGenHandler1_ignore {W S O A} (h : GenHandler W S O A) (s : S) : list O * S	:= let '(_, os, d, _) := runGenHandler s h in (os, d).	Definition	runGenHandler1_ignore	Core	theories/Core/HandlerMonad.v	[ "Coq", "List", "ListNotations" ]	[ "GenHandler", "runGenHandler" ]	for single node semantics	https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
nop {W S O : Type}	:= @ret W S O _ tt.	Definition	nop	Core	theories/Core/HandlerMonad.v	[ "Coq", "List", "ListNotations" ]	[ "ret" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
"a >> b"	:= (bind a (fun _ => b)) (at level 50).	Notation	a >> b	Core	theories/Core/HandlerMonad.v	[ "Coq", "List", "ListNotations" ]	[ "bind" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
"x <- c1 ;; c2"	:= (@bind _ _ _ _ _ c1 (fun x => c2)) (at level 100, c1 at next level, right associativity).	Notation	x <- c1 ;; c2	Core	theories/Core/HandlerMonad.v	[ "Coq", "List", "ListNotations" ]	[ "bind" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
"e1 ;; e2"	:= (_ <- e1 ;; e2) (at level 100, right associativity).	Notation	e1 ;; e2	Core	theories/Core/HandlerMonad.v	[ "Coq", "List", "ListNotations" ]	[]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
when {W S O A} (b : bool) (m : GenHandler W S O A) : GenHandler W S O unit	:= if b then m ;; ret tt else nop.	Definition	when	Core	theories/Core/HandlerMonad.v	[ "Coq", "List", "ListNotations" ]	[ "GenHandler", "nop", "ret" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
monad_unfold	:= repeat unfold runGenHandler_ignore, runGenHandler, runGenHandler1_ignore, bind, send, write_output, get, when, put, nop, modify, ret in *.	Ltac	monad_unfold	Core	theories/Core/HandlerMonad.v	[ "Coq", "List", "ListNotations" ]	[ "bind", "get", "modify", "nop", "put", "ret", "runGenHandler", "runGenHandler1_ignore", "runGenHandler_ignore", "send", "when", "write_output" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
InverseTraceRelation `{State : Type} `{Event : Type} (step : step_relation State Event)	:= { init : State; T : (list Event) -> Prop; R : State -> Prop; R_dec : forall s, {R s} + {~ R s}; T_monotonic : forall tr o, T tr -> T (tr ++ o); R_false_init : ~ R init; R_implies_T : forall s s' o tr, refl_trans_1n_trace step init s tr -> ~ R s ->...	Class	InverseTraceRelation	Core	theories/Core/InverseTraceRelations.v	[ "Coq", "List", "Verdi", "Net", "StructTact", "StructTactics" ]	[ "refl_trans_1n_trace", "step_relation" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
inverse_trace_relations_work : forall s tr, refl_trans_1n_trace step init s tr -> R s -> T tr.	Proof using. intros. find_apply_lem_hyp refl_trans_1n_n1_trace. remember init as s'. induction H. - subst. exfalso. pose R_false_init; auto. - subst. concludes. destruct (R_dec x'); intuition eauto using T_monotonic, refl_trans_n1_1n_trace, R_implies_T. Qed.	Theorem	inverse_trace_relations_work	Core	theories/Core/InverseTraceRelations.v	[ "Coq", "List", "Verdi", "Net", "StructTact", "StructTactics" ]	[ "refl_trans_1n_n1_trace", "refl_trans_1n_trace", "refl_trans_n1_1n_trace" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
LabeledMultiParams (P : BaseParams)	:= { lb_name : Type ; lb_msg : Type ; lb_msg_eq_dec : forall x y : lb_msg, {x = y} + {x <> y} ; lb_name_eq_dec : forall x y : lb_name, {x = y} + {x <> y} ; lb_nodes : list lb_name ; lb_all_names_nodes : forall n, In n lb_nodes ; lb_no_dup_nodes : NoDup lb_nodes ; label : Type ; lab...	Class	LabeledMultiParams	Core	theories/Core/LabeledNet.v	[ "Verdi", "InfSeqExt", "infseq", "exteq", "Ssrexport" ]	[ "BaseParams", "data", "input", "output" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
unlabeled_net_handlers me src m st	:= let '(lb, out, st', ps) := lb_net_handlers me src m st in (out, st', ps).	Definition	unlabeled_net_handlers	Core	theories/Core/LabeledNet.v	[ "Verdi", "InfSeqExt", "infseq", "exteq", "Ssrexport" ]	[ "src" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
unlabeled_input_handlers me inp st	:= let '(lb, out, st', ps) := lb_input_handlers me inp st in (out, st', ps).	Definition	unlabeled_input_handlers	Core	theories/Core/LabeledNet.v	[ "Verdi", "InfSeqExt", "infseq", "exteq", "Ssrexport" ]	[]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
unlabeled_multi_params : MultiParams base_params	:= { name := lb_name ; msg := lb_msg ; msg_eq_dec := lb_msg_eq_dec ; name_eq_dec := lb_name_eq_dec ; nodes := lb_nodes ; all_names_nodes := lb_all_names_nodes ; no_dup_nodes := lb_no_dup_nodes ; init_handlers := lb_init_handlers; net_handlers := unlabeled_net_handlers ; input_h...	Instance	unlabeled_multi_params	Core	theories/Core/LabeledNet.v	[ "Verdi", "InfSeqExt", "infseq", "exteq", "Ssrexport" ]	[ "MultiParams", "all_names_nodes", "base_params", "msg", "msg_eq_dec", "name", "name_eq_dec", "no_dup_nodes", "nodes", "unlabeled_input_handlers", "unlabeled_net_handlers" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
lb_step_relation	:= A -> L -> A -> list trace -> Prop.	Definition	lb_step_relation	Core	theories/Core/LabeledNet.v	[ "Verdi", "InfSeqExt", "infseq", "exteq", "Ssrexport" ]	[]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
lb_step_ex (step : lb_step_relation) (l : L) (a : A) : Prop	:= exists a' tr, step a l a' tr.	Definition	lb_step_ex	Core	theories/Core/LabeledNet.v	[ "Verdi", "InfSeqExt", "infseq", "exteq", "Ssrexport" ]	[ "lb_step_relation" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
event	:= { evt_a : A ; evt_l : L ; evt_trace : list trace }.	Record	event	Core	theories/Core/LabeledNet.v	[ "Verdi", "InfSeqExt", "infseq", "exteq", "Ssrexport" ]	[]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
enabled (step : lb_step_relation) (l : L) (e : event) : Prop	:= lb_step_ex step l (evt_a e).	Definition	enabled	Core	theories/Core/LabeledNet.v	[ "Verdi", "InfSeqExt", "infseq", "exteq", "Ssrexport" ]	[ "event", "lb_step_ex", "lb_step_relation" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b
occurred (l : L) (e : event) : Prop	:= l = evt_l e.	Definition	occurred	Core	theories/Core/LabeledNet.v	[ "Verdi", "InfSeqExt", "infseq", "exteq", "Ssrexport" ]	[ "event" ]		https://github.com/uwplse/verdi	7e1641b758d8f0032aa7de63620bc115330e0a6b

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Coq-Verdi

Structured dataset from Verdi — Distributed systems verification.

Source

Repository: https://github.com/uwplse/verdi
Commit: 7e1641b758d8f0032aa7de63620bc115330e0a6b
Files: 40
License: bsd-2-clause

Schema

Column	Type	Description
statement	string	Declaration signature/claim with the leading keyword removed (verbatim slice); the full declaration minus its proof
proof	string	Verbatim proof/body, empty if the declaration has none
type	string	Declaration keyword
symbolic_name	string	Declaration identifier
library	string	Sub-library
filename	string	Repository-relative source path
imports	list[string]	File-level `Require`/`Import` modules
deps	list[string]	Intra-corpus identifiers referenced
docstring	string	Preceding documentation comment, empty if absent
source_url	string	Upstream repository
commit	string	Upstream commit extracted

Statistics

Entries: 1,035
With proof: 989 (95.6%)
With docstring: 20 (1.9%)
Libraries: 3

By type

Type	Count
Lemma	428
Definition	292
Theorem	68
Instance	64
Class	40
Inductive	37
Parameter	35
Corollary	14
Ltac	13
Record	12
Hypothesis	11
Fixpoint	10
Notation	6
Example	4
CoInductive	1

Example

dup_drop_step : list A -> list A -> Prop
:=
  | DDS_dup : forall l p,
      In p l ->
      dup_drop_step l (p :: l)
  | DDS_drop : forall xs p ys,
      dup_drop_step (xs ++ p :: ys) (xs ++ ys).

type: Inductive | symbolic_name: dup_drop_step | theories/Core/DupDropReordering.v

Use

Each declaration is split into a statement (signature/claim) and a proof (body) that are disjoint and together form the complete declaration, for proof modeling, autoformalization, retrieval, and dependency analysis via deps.

Citation

@misc{coq_verdi_dataset,
  title  = {Coq-Verdi},
  author = {Norton, Charles},
  year   = {2026},
  note   = {Extracted from https://github.com/uwplse/verdi, commit 7e1641b758d8},
  url    = {https://huggingface.co/datasets/phanerozoic/Coq-Verdi}
}

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