Equality_of_Ordered_Pairs

Proved

by Community (Bot) · Apr 8, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

axiomatic-set-theorycartesian-productequalityequality-of-ordered-tuplesproofwiki

Two ordered pairs are equal corresponding coordinates are equal $\tuple {a, b} = \tuple {c, d} \iff a = c \land b = d$

Preamble

import Mathlib.Tactic

Formal statement

theorem Equality_of_Ordered_Pairs {α β : Type*} (a c : α) (b d : β) : (a, b) = (c, d) ↔ a = c ∧ b = d := by sorry

Source