38 lines
1 KiB
Text
38 lines
1 KiB
Text
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/-
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1. A ∧ B → C ==> { A → B → C }
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2. A ∨ B → C ==> { A → C, B → C }
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3. A → B ∧ C ==> { A → C, A → C }
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4. A ↔ B ==> { (A → B) ∧ (B → A) }
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5. Push negations inside ∧ and ∨ (when using classical)
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6. ite A B C ==> { A → B, ¬ A → C }
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-/
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open simplifier.unit_simp
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set_option simplify.max_steps 100000
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namespace vars
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variables {A B C D E F G : Prop}
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variables [A_dec : decidable A]
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#simplify iff env 0 A → B ∧ C
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#simplify iff env 0 A → B ∧ C ∧ D
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#simplify iff env 0 A → B ∧ C → D
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#simplify iff env 0 A → B ∧ C → D ∧ E
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#simplify iff env 0 A → B ∧ C → D ∨ E → F ∧ G
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#simplify iff env 0 A → B ∧ C → D ∨ E → ((F → G) ∧ (G → F))
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end vars
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namespace cs
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constants {A B C D E F G : Prop}
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constants [A_dec : decidable A]
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attribute A_dec [instance]
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#simplify iff env 0 ite A B C
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#simplify iff env 0 ite A B C → B ∧ C
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#simplify iff env 0 A → (ite A B C)
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#simplify iff env 0 A → B ∧ (ite A B C) → D ∨ E → ((F → G) ∧ (G → F))
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end cs
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