Theorems · Theorem
IsEmpty.forall_iff
∀ {α : Sort u} [IsEmpty α] {p : α → Prop}, (∀ (a : α), p a) ↔ True- Defined in
- Mathlib.Logic.IsEmpty.Defs
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- IsEmpty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsEmptystatement and proof · cited by 759
- isEmptyElimproof · cited by 59
Cited by39
Results whose statement or proof uses this declaration.
- tsum_fintypeproof · cited by 38
- Finset.sum_dite_eq'proof · cited by 21
- Equiv.hasSum_iffproof · cited by 18
- Finset.sum_dite_eqproof · cited by 12
- Finset.sum_eq_add_sum_sdiff_singleton_of_memproof · cited by 9
- hasSum_sumproof · cited by 4
- WithTop.le_iff_forallproof · cited by 4
- Finset.inf_eq_top_iffproof · cited by 3
- Multiset.le_infproof · cited by 3
- AddSubgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3
- List.single_le_sumproof · cited by 3
- AddAction.IsFixedBlock.isBlockproof · cited by 3