Theorems · Theorem · order theory
inf_himp
∀ {α : Type u_2} [inst : GeneralizedHeytingAlgebra α] (a b : α), a ⊓ (a ⇨ b) = a ⊓ bp ∧ (p → q) ↔ p ∧ q
- Defined in
- Mathlib.Order.Heyting.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext
- Assumes
- GeneralizedHeytingAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- inf_le_leftproof · cited by 286
- HImp.himpstatement and proof · cited by 153
- inf_commproof · cited by 139
- le_infproof · cited by 107
- GeneralizedHeytingAlgebrastatement and proof · cited by 68
- inf_le_inf_leftproof · cited by 25
- le_himp_iffproof · cited by 19
- le_himpproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- himp_inf_selfproof · cited by 3
- compl_bihimp_selfproof · cited by 2