prod_trans — Mathlib

English

The product respects transitivity: (e.prod e').trans (f.prod f') = (e.trans f).prod (e'.trans f').

Русский

Произведение respects транзитивность: (e.prod e').trans (f.prod f') = (e.trans f).prod (e'.trans f').

LaTeX

$$$ (e.prod e').trans (f.prod f') = (e.trans f).prod (e'.trans f') $$$

Lean4

@[simp, mfld_simps]
theorem prod_trans {η : Type*} {ε : Type*} (e : PartialEquiv α β) (f : PartialEquiv β γ) (e' : PartialEquiv δ η)
    (f' : PartialEquiv η ε) : (e.prod e').trans (f.prod f') = (e.trans f).prod (e'.trans f') := by ext ⟨x, y⟩ <;> simp;
  tauto

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