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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_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_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_P.
all: 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_P.
all: apply (P_triv Type).
Qed.
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