himp_bihimp_eq_inf — Mathlib

English

The implication of a to bihimp(b, c) equals the infimum of bihimp(a(b ∧ c), b) and bihimp(a(b ∧ c), c).

Русский

Импликация от a к bihimp(b,c) равна наименьшему из bihimp(a ∧ c, b) и bihimp(a ∧ b, c).

LaTeX

$$$\operatorname{himp}(a, \operatorname{bihimp}(b,c)) = \min\big( \operatorname{himp}(a \wedge c, b), \operatorname{himp}(a \wedge b, c) \big)$$$

Lean4

@[simp]
theorem himp_bihimp_eq_inf : (b ⇨ a) ⇔ b = a ⊓ b :=
  @sdiff_symmDiff_eq_sup αᵒᵈ _ _ _

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