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fix(library/tactic/congruence/congruence_closure): missing proof construction step

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This commit is contained in:
Leonardo de Moura 2016-12-24 08:43:04 -08:00
parent a176bd324d
commit 424a6acb68
2 changed files with 73 additions and 1 deletions
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13
src/library/tactic/congruence/congruence_closure.cpp
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@ -864,7 +864,18 @@ expr congruence_closure::mk_congr_proof_core(expr const & lhs, expr const & rhs,
r = mk_eq_of_heq(m_ctx, r);
else if (!lemma->m_heq_result && heq_proofs)
r = mk_heq_of_eq(m_ctx, r);
return r;
if (lhs_fn == rhs_fn ||
m_ctx.is_def_eq(lhs_fn, rhs_fn))
return r;
/* Convert r into a proof of lhs = rhs using eq.rec and
the proof that lhs_fn = rhs_fn */
expr lhs_fn_eq_rhs_fn = *get_eq_proof(lhs_fn, rhs_fn);
type_context::tmp_locals locals(m_ctx);
expr x = locals.push_local("_x", m_ctx.infer(lhs_fn));
expr motive_rhs = mk_app(x, rhs_args);
expr motive = heq_proofs ? mk_heq(m_ctx, lhs, motive_rhs) : mk_eq(m_ctx, lhs, motive_rhs);
motive = locals.mk_lambda(motive);
return mk_eq_rec(m_ctx, motive, r, lhs_fn_eq_rhs_fn);
} else {
/* This branch builds congruence proofs that handle equality between functions.
The proof is created using congr_arg/congr_fun/congr lemmas.

61
tests/lean/run/cc5.lean Normal file
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@ -0,0 +1,61 @@
universes l1 l2 l3 l4 l5 l6
constants (A : Type l1) (B : A → Type l2) (C : ∀ (a : A) (ba : B a), Type l3)
(D : ∀ (a : A) (ba : B a) (cba : C a ba), Type l4)
(E : ∀ (a : A) (ba : B a) (cba : C a ba) (dcba : D a ba cba), Type l5)
(F : ∀ (a : A) (ba : B a) (cba : C a ba) (dcba : D a ba cba) (edcba : E a ba cba dcba), Type l6)
(C_ss : ∀ a ba, subsingleton (C a ba))
(a1 a2 a3 : A)
(mk_B1 mk_B2 : ∀ a, B a)
(mk_C1 mk_C2 : ∀ {a} ba, C a ba)
(tr_B : ∀ {a}, B a → B a)
(x y z : A → A)
(f f' : ∀ {a : A} {ba : B a} (cba : C a ba), D a ba cba)
(g : ∀ {a : A} {ba : B a} {cba : C a ba} (dcba : D a ba cba), E a ba cba dcba)
(h : ∀ {a : A} {ba : B a} {cba : C a ba} {dcba : D a ba cba} (edcba : E a ba cba dcba), F a ba cba dcba edcba)
attribute [instance] C_ss
open tactic
example : ∀ (a a' : A), a == a' → mk_B1 a == mk_B1 a' :=
by cc
example : ∀ (a a' : A), a == a' → mk_B2 a == mk_B2 a' :=
by cc
example : a1 == y a2 → mk_B1 a1 == mk_B1 (y a2) :=
by cc
example : a1 == x a2 → a2 == y a1 → mk_B1 (x (y a1)) == mk_B1 (x (y (x a2))) :=
by cc
example : a1 == y a2 → mk_B1 a1 == mk_B2 (y a2) → f (mk_C1 (mk_B2 a1)) == f (mk_C2 (mk_B1 (y a2))) :=
by cc
example : a1 == y a2 → tr_B (mk_B1 a1) == mk_B2 (y a2) → f (mk_C1 (mk_B2 a1)) == f (mk_C2 (tr_B (mk_B1 (y a2)))) :=
by cc
example : a1 == y a2 → mk_B1 a1 == mk_B2 (y a2) → g (f (mk_C1 (mk_B2 a1))) == g (f (mk_C2 (mk_B1 (y a2)))) :=
by cc
example : a1 == y a2 → tr_B (mk_B1 a1) == mk_B2 (y a2) → g (f (mk_C1 (mk_B2 a1))) == g (f (mk_C2 (tr_B (mk_B1 (y a2))))) :=
by cc
example : a1 == y a2 → a2 == z a3 → a3 == x a1 → mk_B1 a1 == mk_B2 (y (z (x a1))) →
f (mk_C1 (mk_B2 (y (z (x a1))))) == f' (mk_C2 (mk_B1 a1)) →
g (f (mk_C1 (mk_B2 (y (z (x a1)))))) == g (f' (mk_C2 (mk_B1 a1))) :=
by cc
example : a1 == y a2 → a2 == z a3 → a3 == x a1 → mk_B1 a1 == mk_B2 (y (z (x a1))) →
f (mk_C1 (mk_B2 (y (z (x a1))))) == f' (mk_C2 (mk_B1 a1)) →
f' (mk_C1 (mk_B1 a1)) == f (mk_C2 (mk_B2 (y (z (x a1))))) →
g (f (mk_C1 (mk_B1 (y (z (x a1)))))) == g (f' (mk_C2 (mk_B2 a1))) :=
by cc
example : a1 == y a2 → a2 == z a3 → a3 == x a1 → tr_B (mk_B1 a1) == mk_B2 (y (z (x a1))) →
f (mk_C1 (mk_B2 (y (z (x a1))))) == f' (mk_C2 (tr_B (mk_B1 a1))) →
f' (mk_C1 (tr_B (mk_B1 a1))) == f (mk_C2 (mk_B2 (y (z (x a1))))) →
g (f (mk_C1 (tr_B (mk_B1 (y (z (x a1))))))) == g (f' (mk_C2 (mk_B2 a1))) :=
by cc