Theorems · Theorem · logic and foundations
Function.Embedding.trans_apply
∀ {α : Sort u_1} {β : Sort u_2} {γ : Sort u_3} (f : α ↪ β) (g : β ↪ γ) (a : α), (f.trans g) a = g (f a)- Defined in
- Mathlib.Logic.Embedding.Basic
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
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.
- DFunLike.coestatement and proof · cited by 62,936
- Function.Embeddingstatement and proof · cited by 988
- Function.Embedding.transstatement and proof · cited by 83
Cited by25
Results whose statement or proof uses this declaration.
- Nat.mem_finMulAntidiagproof · cited by 7
- Fin.cycleIcc_of_le_of_leproof · cited by 5
- Fin.Embedding.restrictSurjective_of_add_le_ENatCardproof · cited by 4
- Fin.cycleIcc_of_gtproof · cited by 3
- Fin.range_natAdd_castLEEmbproof · cited by 3
- nivenproof · cited by 2
- Function.Embedding.exists_of_card_le_finsetproof · cited by 2
- SubMulAction.exists_smul_of_last_eqproof · cited by 1
- SubAddAction.ofFixingAddSubgroup.append_leftproof · cited by 1
- SubAddAction.ofFixingAddSubgroup.append_rightproof · cited by 1
- AddAction.IsPretransitive.of_embeddingproof · cited by 1