lean2/tests/lean/simp3.lean.expected.out
Leonardo de Moura 97ead50a3e feat(builtin/Nat): flip orientation of associativity axioms for + and *
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-20 15:38:00 -08:00

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Set: pp::colors
Set: pp::unicode
Defined: double
9
2 + 2 + (2 + 2) + 1 ≥ 3
3 ≤ 2 * 2 + (2 * 2 + (2 * 2 + (2 * 2 + 1)))
Assumed: a
Assumed: b
Assumed: c
Assumed: d
Imported 'if_then_else'
a * c + (a * d + (b * c + b * d))
trans (Nat::distributel a b (c + d))
(trans (congr (congr2 Nat::add (Nat::distributer a c d)) (Nat::distributer b c d))
(Nat::add_assoc (a * c) (a * d) (b * c + b * d)))
Proved: congr2_congr1
Proved: congr2_congr2
Proved: congr1_congr2
trans (congr (congr2 eq
(congr1 10
(congr2 Nat::add (trans (congr2 (ite (a > 0) b) (Nat::add_zeror b)) (if_a_a (a > 0) b)))))
(congr1 10 (congr2 Nat::add (if_a_a (a > 0) b))))
(eq_id (b + 10))
let κ::1 := congr2 (λ x : , eq ((λ x : , x + 10) x))
(trans (congr2 (ite (a > 0) b) (Nat::add_zeror b)) (if_a_a (a > 0) b))
in trans (congr κ::1 (congr2 (λ x : , x + 10) (if_a_a (a > 0) b))) (eq_id (b + 10))
a * a + (a * b + (b * a + b * b))
→ ⊥ refl ( → ⊥)
refl ()
⊥ → ⊥ refl (⊥ → ⊥)
⊥ refl ⊥