Theorems · Theorem · group theory
Submonoid.mem_saturation_iff
∀ {M : Type u_1} [inst : CommMonoid M] {s : Submonoid M} {x : M}, x ∈ s.saturation ↔ ∃ y, x * y ∈ s- Cited by
- 0 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoid
Around this declaration
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- Submonoidstatement and proof · cited by 3,086
- CommMonoidstatement and proof · cited by 2,264
- mul_assocproof · cited by 1,667
- mul_left_commproof · cited by 184
- MulMemClass.mul_memproof · cited by 173
- mul_mul_mul_commproof · cited by 65
- SaturatedSubmonoidstatement · cited by 29
- Submonoid.saturationstatement and proof · cited by 18
- SaturatedSubmonoid.mulSaturatedproof · cited by 2
- Submonoid.le_toSubmonoid_saturationproof · cited by 2
- Submonoid.saturation_inductionproof · cited by 1
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