Theorems · Theorem
Equiv.exists_congr_left
∀ {α : Sort u} {β : Sort v} {p : α → Prop} (e : α ≃ β), (∃ a, p a) ↔ ∃ b, p (e.symm b)- Defined in
- Mathlib.Logic.Equiv.Defs
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Equivstatement and proof · cited by 8,337
- Equiv.symmstatement and proof · cited by 3,681
- Equiv.exists_congr_rightproof · cited by 9
Cited by33
Results whose statement or proof uses this declaration.
- QuotientAddGroup.leftRel_applyproof · cited by 20
- dvd_negproof · cited by 19
- QuotientGroup.leftRel_applyproof · cited by 17
- Equiv.exists_congrproof · cited by 13
- NumberField.absNorm_differentIdealproof · cited by 4
- Equiv.Perm.sameCycle_apply_leftproof · cited by 4
- Equiv.Perm.sameCycle_zpow_leftproof · cited by 4
- neg_dvdproof · cited by 3
- Set.empty_definable_iffproof · cited by 2
- Equiv.Perm.sameCycle_invproof · cited by 2
- Module.Basis.mem_submodule_iff'proof · cited by 2
- PowerBasis.mem_span_pow'proof · cited by 2