Theorems · Theorem · order theory
sup_himp_distrib
∀ {α : Type u_2} [inst : GeneralizedHeytingAlgebra α] (a b c : α), a ⊔ b ⇨ c = (a ⇨ c) ⊓ (b ⇨ c)- Defined in
- Mathlib.Order.Heyting.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
- 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 and proof · cited by 153
- GeneralizedHeytingAlgebrastatement and proof · cited by 68
- eq_of_forall_le_iffproof · cited by 65
- sup_le_iffproof · cited by 58
- le_inf_iffproof · cited by 48
- le_himp_commproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- compl_sup_distribproof · cited by 5
- sup_himp_self_leftproof · cited by 2
- sup_himp_self_rightproof · cited by 1