Theorems · Theorem · order theory
himp_self
∀ {α : Type u_2} [inst : GeneralizedHeytingAlgebra α] {a : α}, a ⇨ a = ⊤p → p
- Defined in
- Mathlib.Order.Heyting.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- GeneralizedHeytingAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- inf_le_rightproof · cited by 238
- top_le_iffproof · cited by 175
- HImp.himpstatement · cited by 153
- GeneralizedHeytingAlgebrastatement and proof · cited by 68
- le_himp_iffproof · cited by 19
Cited by6
Results whose statement or proof uses this declaration.
- compl_botproof · cited by 8
- bihimp_selfproof · cited by 2
- sup_himp_self_leftproof · cited by 2
- sup_himp_self_rightproof · cited by 1
- Codisjoint.himp_inf_cancel_rightproof · cited by 0
- Codisjoint.himp_inf_cancel_leftproof · cited by 0