pair_zip_pair — Mathlib

English

The zip of two pair-chains is a pair-chain of pairs: (pair a1 a2 ha).zip (pair b1 b2 hb) equals pair (a1,b1) (a2,b2) with the appropriate Prod-order.

Русский

Зип двух цепей-пар является цепью пар: zip(pair a1 a2 ha, pair b1 b2 hb) = pair (a1,b1) (a2,b2) ⟨ha, hb⟩.

LaTeX

$$$$ (\\text{pair } a_1 a_2 ha) .\\text{zip} (\\text{pair } b_1 b_2 hb) = \\text{pair } (a_1,b_1) (a_2,b_2) (\\text{Prod.le\_def}.2 \\langle ha, hb \\rangle). $$$$

Lean4

@[simp]
theorem pair_zip_pair (a₁ a₂ : α) (b₁ b₂ : β) (ha hb) :
    (pair a₁ a₂ ha).zip (pair b₁ b₂ hb) = pair (a₁, b₁) (a₂, b₂) (Prod.le_def.2 ⟨ha, hb⟩) := by unfold Chain; ext n : 2;
  cases n <;> rfl

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