Theorems · Theorem · logic and foundations
Subtype.coe_ne_coe
∀ {α : Sort u_1} {p : α → Prop} {a b : Subtype p}, ↑a ≠ ↑b ↔ a ≠ b- Defined in
- Mathlib.Data.Subtype
- Cited by
- 27 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 by27
Results whose statement or proof uses this declaration.
- finrank_span_singletonproof · cited by 16
- AnalyticOnNhd.isClopen_setOfPred_analyticOrderAt_eq_topproof · cited by 2
- Real.strictConcaveOn_rpowproof · cited by 2
- IsNoetherianRing.isArtinianRing_of_krullDimLE_zeroproof · cited by 2
- MeromorphicOn.isClopen_setOfPred_meromorphicOrderAt_eq_topproof · cited by 2
- Nat.pairwise_coprime_pow_primeFactors_factorizationproof · cited by 1
- Equiv.Perm.Basis.ofPermHomFun_apply_mem_support_cycle_iffproof · cited by 1
- HahnEmbedding.ArchimedeanStrata.iSupIndep_stratumproof · cited by 1
- notMem_iff_exists_ne_and_isConjRootproof · cited by 1
- exists_dist_slope_lt_pairwiseDisjoint_hasSumproof · cited by 1
- Module.FaithfullyFlat.range_le_ker_of_exact_rTensorproof · cited by 1
- LieAlgebra.engel_isBot_of_isMinproof · cited by 1