mk_lt_mk — Mathlib

English

From lt_iff, we have (a1,b1) < (a2,b2) iff a1 < a2 ∧ b1 ≤ b2 or a1 ≤ a2 ∧ b1 < b2.

Русский

Из lt_iff следует: (a1,b1) < (a2,b2) эквивалентно (a1 < a2 ∧ b1 ≤ b2) или (a1 ≤ a2 ∧ b1 < b2).

LaTeX

$$$(a_1,b_1) < (a_2,b_2) \iff (a_1 < a_2 \land b_1 \le b_2) \lor (a_1 \le a_2 \land b_1 < b_2)$$$

Lean4

@[simp]
theorem mk_lt_mk : (a₁, b₁) < (a₂, b₂) ↔ a₁ < a₂ ∧ b₁ ≤ b₂ ∨ a₁ ≤ a₂ ∧ b₁ < b₂ :=
  lt_iff

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