Submonoid.mem_closure_pair

∀ {A : Type u_4} [inst : CommMonoid A] (a b c : A), c ∈ Submonoid.closure {a, b} ↔ ∃ m n, a ^ m * b ^ n = c

An element is in the closure of a two-element set if it is a linear combination of those two elements.

Defined in: Mathlib.Algebra.Group.Submonoid.Membership
Cited by: 0 results in Mathlib
Foundations: Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommMonoid

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