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