lean2/tests/lean/simplifier9.lean

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-- Rewriting with (tmp)-local hypotheses
import logic.quantifiers
attribute imp_congr [congr]
attribute forall_congr [congr]
universe l
constants (T : Type.{l}) (P Q : T → Prop)
set_option simplify.max_steps 50000
constants (x y : T)
#simplify iff env 0 x = y → x = y
#simplify iff env 0 T → x = y → x = y
#simplify iff env 0 ∀ z : T, x = z → x = y
#simplify iff env 0 ∀ z : T, z = x → x = z
#simplify iff env 0 ∀ (z w : T), x = y → x = y
#simplify iff env 0 ∀ (z w : T), x = y → P x
#simplify iff env 0 ∀ (H : ∀ x, P x ↔ Q x), P x
#simplify iff env 0 ∀ (p : Prop) (H : ∀ x, P x ↔ Q x) (q : Prop), P x
#simplify iff env 0 ∀ (p : Prop) (H : ∀ x, P x ↔ Q x), p P x
#simplify iff env 0 (∀ (x : T), P x ↔ Q x) → P x
#simplify iff env 0 ∀ (x y : T), (∀ (x : T), P x ↔ Q x) → P x
#simplify iff env 0 ∀ (x z : T), x = z → P x
#simplify iff env 0 ∀ (x y z : T), x = y → y = z → P x
#simplify iff env 0 ∀ (x z : T), x = z → (∀ (w : T), P w ↔ Q w) → P x