lean2/tests/lean/simplifier_unit_preprocess.lean

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