Theorems · Theorem · order theory
GeneralizedHeytingAlgebra.le_himp_iff
∀ {α : Type u_4} [self : GeneralizedHeytingAlgebra α] (a b c : α), a ≤ b ⇨ c ↔ a ⊓ b ≤ c(a ⇨ ·) is right adjoint to (a ⊓ ·)
- Defined in
- Mathlib.Order.Heyting.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 3 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.
- HImp.himpstatement · cited by 153
- GeneralizedHeytingAlgebrastatement and proof · cited by 68
- Lattice.infstatement · cited by 18
- Lattice.inf_le_leftstatement · cited by 12
- Lattice.inf_le_rightstatement · cited by 12
- Lattice.le_infstatement · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- le_himp_iffproof · cited by 19