Theorems · Theorem · group theory
Prod.fst_mul_snd
∀ {M : Type u_3} {N : Type u_4} [inst : MulOneClass M] [inst_1 : MulOneClass N] (p : M × N), (p.1, 1) * (1, p.2) = p- Defined in
- Mathlib.Algebra.Group.Prod
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- MulOneClassMulOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- MulOneClassstatement and proof · cited by 1,018
Cited by6
Results whose statement or proof uses this declaration.
- Equiv.Perm.OnCycleFactors.sign_kerParam_apply_applyproof · cited by 2
- Submonoid.prod_bot_sup_bot_prodproof · cited by 2
- Monoid.Coprod.toProd_surjectiveproof · cited by 0
- Equiv.Perm.OnCycleFactors.cycleType_kerParam_apply_applyproof · cited by 0
- Subring.prod_bot_sup_bot_prodproof · cited by 0
- Subsemiring.prod_bot_sup_bot_prodproof · cited by 0