43 lines
1.1 KiB
Text
43 lines
1.1 KiB
Text
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Set: pp::colors
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Set: pp::unicode
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Assumed: a
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Assumed: b
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Assumed: c
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a + (b + 0) + a
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=====>
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Visit, depth: 1, a + (b + 0) + a
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Visit, depth: 2, Nat::add
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Visit, depth: 2, a + (b + 0)
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Visit, depth: 3, Nat::add
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Visit, depth: 3, a
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Step: a ===> a
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Visit, depth: 3, b + 0
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Visit, depth: 4, Nat::add
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Visit, depth: 4, b
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Step: b ===> b
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Visit, depth: 4, 0
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Rewrite using: Nat::add_zeror
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b + 0 ===> b
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Step: b + 0 ===> b
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Visit, depth: 3, a + b
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Visit, depth: 4, Nat::add
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Step: a + b ===> a + b
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Step: a + (b + 0) ===> a + b
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Rewrite using: Nat::add_assoc
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a + b + a ===> a + (b + a)
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Visit, depth: 2, a + (b + a)
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Visit, depth: 3, Nat::add
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Visit, depth: 3, b + a
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Visit, depth: 4, Nat::add
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Rewrite using: Nat::add_comm
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b + a ===> a + b
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Step: b + a ===> a + b
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Visit, depth: 3, a + (a + b)
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Visit, depth: 4, Nat::add
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Step: a + (a + b) ===> a + (a + b)
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Step: a + (b + a) ===> a + (a + b)
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Step: a + (b + 0) + a ===> a + (a + b)
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a + (a + b)
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trans (trans (congr1 a (congr2 Nat::add (congr2 (Nat::add a) (Nat::add_zeror b)))) (Nat::add_assoc a b a))
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(congr2 (Nat::add a) (Nat::add_comm b a))
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