Theorems · Theorem · logic and foundations
Subtype.coe_inj
∀ {α : Sort u_1} {p : α → Prop} {a b : Subtype p}, ↑a = ↑b ↔ a = b- Defined in
- Mathlib.Data.Subtype
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Subtype.coe_injectiveproof · cited by 205
Cited by33
Results whose statement or proof uses this declaration.
- Subtype.val_injproof · cited by 9
- NNRat.coe_injproof · cited by 5
- Equiv.Perm.Basis.ofPermHomFun_apply_of_cycleOf_memproof · cited by 5
- Valuation.Uniformizer.is_generatorproof · cited by 4
- ComplementedLattice.isStronglyAtomicproof · cited by 2
- LinearEquiv.mem_dilatransvections_iff_rankproof · cited by 2
- Complementeds.coe_injproof · cited by 2
- disjoint_subtype_iffproof · cited by 2
- Setoid.IsPartition.ncard_eq_finsumproof · cited by 2
- SubAddAction.ofFixingAddSubgroup_insert_map_bijectiveproof · cited by 2
- OrdinalApprox.exists_lfpApprox_eq_lfpApproxproof · cited by 2