Theorems · Theorem · group theory
Submonoid.saturation_le_of_le
∀ {M : Type u_1} [inst : MulOneClass M] {a : Submonoid M} {b : SaturatedSubmonoid M},
a ≤ b.toSubmonoid → a.saturation ≤ bAlias of the reverse direction of Submonoid.saturation_le_iff_le.
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- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
- Assumes
- MulOneClass
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Submonoidstatement and proof · cited by 3,086
- MulOneClassstatement and proof · cited by 1,018
- SaturatedSubmonoidstatement and proof · cited by 29
- Submonoid.saturationstatement · cited by 18
- SaturatedSubmonoid.toSubmonoidstatement · cited by 14
- Submonoid.saturation_le_iff_leproof · cited by 1
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