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Equality_of_Division_Products_v2

Proved

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

divisionproofwikirings

Let R be a commutative ring with unity. Then a/c = b/d iff ad = bc.

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem Equality_of_Division_Products_v2 {F : Type _} [Field F] (a b c d : F) (hc : c ≠ 0) (hd : d ≠ 0) : a / c = b / d ↔ a * d = b * c := by sorry
Source
https://proofwiki.org/wiki/Equality_of_Division_Products

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