Theorems · Theorem · group theory
DivisibleHull.mk_eq_mk
∀ {M : Type u_1} [inst : AddCommMonoid M] {m m' : M} {s s' : ℕ+},
DivisibleHull.mk m s = DivisibleHull.mk m' s' ↔ ∃ u, ↑u • ↑s' • m = ↑u • ↑s • m'- Defined in
- Mathlib.GroupTheory.DivisibleHull
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- nonZeroDivisorsproof · cited by 895
- PNatstatement and proof · cited by 392
- PNat.valstatement and proof · cited by 226
- MulEquiv.toEquivproof · cited by 126
- Equiv.exists_congr_leftproof · cited by 33
- DivisibleHullstatement · cited by 30
- OrderMonoidIso.toMulEquivproof · cited by 20
- DivisibleHull.mkstatement · cited by 19
- LocalizedModule.mk_eqproof · cited by 15
- PNat.equivNonZeroDivisorsNatproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- DivisibleHull.mk_add_mk_leftproof · cited by 3