Theorems · Theorem · commutative algebra
map_prime_of_factor_orderIso
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [IsCancelMulZero M] {N : Type u_2} [inst_2 : CommMonoidWithZero N]
[UniqueFactorizationMonoid N] [inst_4 : UniqueFactorizationMonoid M] {m p : Associates M} {n : Associates N},
n ≠ 0 →
∀ (hp : p ∈ UniqueFactorizationMonoid.normalizedFactors m) (d : ↑(Set.Iic m) ≃o ↑(Set.Iic n)), Prime ↑(d ⟨p, ⋯⟩)- Defined in
- Mathlib.RingTheory.ChainOfDivisors
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites38
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- Bot.botproof · cited by 4,720
- Unitsstatement · cited by 2,804
- Multisetstatement · cited by 2,627
- le_of_ltproof · cited by 1,175
- Set.Iicstatement and proof · cited by 1,111
- OrderBotproof · cited by 1,055
- le_transproof · cited by 985
- CommMonoidWithZerostatement and proof · cited by 913
- OrderIsostatement and proof · cited by 874
Cited by2
Results whose statement or proof uses this declaration.
- mem_normalizedFactors_factor_dvd_iso_of_mem_normalizedFactorsproof · cited by 1
- mem_normalizedFactors_factor_orderIso_of_mem_normalizedFactorsproof · cited by 1