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Lemma test_nofail_like_all1 :
True /\ False.
Proof.
split.
all: trivial.
Admitted.
Lemma test_nofail_like_all2 :
True /\ False.
Proof.
split.
par: trivial.
Admitted.
Fixpoint fib n := match n with
| O => 1
| S m => match m with
| O => 1
| S o => fib o + fib m end end.
Ltac sleep n :=
try (assert (fib n = S (fib n)) by reflexivity).
(* Tune that depending on your PC *)
Let time := 18.
Axiom P : nat -> Prop.
Axiom P_triv : Type -> forall x, P x.
Ltac solve_P :=
match goal with |- P (S ?X) =>
sleep time; exact (P_triv Type _)
end.
Lemma test_old x : P (S x) /\ P (S x) /\ P (S x) /\ P (S x).
Proof.
repeat split.
idtac "T1: linear".
Time all: solve [solve_P].
Qed.
Lemma test_ok x : P (S x) /\ P (S x) /\ P (S x) /\ P (S x).
Proof.
repeat split.
idtac "T2: parallel".
Time par: solve [solve_P].
Qed.
Lemma test_fail x : P (S x) /\ P x /\ P (S x) /\ P (S x).
Proof.
repeat split.
idtac "T3: linear failure".
Fail Time all: solve solve_P.
all: solve [apply (P_triv Type)].
Qed.
Lemma test_fail2 x : P (S x) /\ P x /\ P (S x) /\ P (S x).
Proof.
repeat split.
idtac "T4: parallel failure".
Fail Time par: solve [solve_P].
all: solve [apply (P_triv Type)].
Qed.
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