Theorems · Theorem · order theory
himp_eq_top_iff
∀ {α : Type u_2} [inst : GeneralizedHeytingAlgebra α] {a b : α}, a ⇨ b = ⊤ ↔ a ≤ bThe deduction theorem in the Heyting algebra model of intuitionistic logic: an implication holds iff the conclusion follows from the hypothesis.
- Defined in
- Mathlib.Order.Heyting.Basic
- Cited by
- 5 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.
- Top.topstatement · cited by 9,680
- top_le_iffproof · cited by 175
- HImp.himpstatement · cited by 153
- GeneralizedHeytingAlgebrastatement and proof · cited by 68
- top_inf_eqproof · cited by 30
- le_himp_iffproof · cited by 19
Cited by5
Results whose statement or proof uses this declaration.
- bot_himpproof · cited by 2
- himp_topproof · cited by 1
- bihimp_eq_topproof · cited by 0
- bihimp_of_geproof · cited by 0
- bihimp_of_leproof · cited by 0