Theorems · Inductive type
HNot
Type u_1 → Type u_1
Syntax typeclass for Heyting negation ￢.
The difference between Compl and HNot is that the former belongs to Heyting algebras,
while the latter belongs to co-Heyting algebras. They are both pseudo-complements, but compl
underestimates while HNot overestimates. In Boolean algebras, they are equal.
See hnot_eq_compl.
- Defined in
- Mathlib.Order.Notation
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 0 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by59
Results whose statement or proof uses this declaration.
- HNot.hnotstatement and proof · cited by 83
- CompletelyDistribLattice.toHNotstatement · cited by 1
- BiheytingAlgebra.toHNotstatement · cited by 1
- Equiv.hnotstatement and proof · cited by 1
- CompleteLinearOrder.toHNotstatement · cited by 1
- CompleteDistribLattice.toHNotstatement · cited by 1
- Order.Coframe.toHNotstatement · cited by 1
- CompletelyDistribLattice.casesOnstatement and proof · cited by 0
- CompletelyDistribLattice.noConfusionproof · cited by 0
- CompletelyDistribLattice.noConfusionTypeproof · cited by 0
- CompletelyDistribLattice.recOnstatement and proof · cited by 0
- BiheytingAlgebra.casesOnstatement and proof · cited by 0