Theorems · Theorem · logic and foundations
not_and_or
∀ {a b : Prop}, ¬(a ∧ b) ↔ ¬a ∨ ¬bOne of de Morgan's laws: the negation of a conjunction is logically equivalent to the disjunction of the negations.
- Defined in
- Mathlib.Logic.Basic
- Cited by
- 82 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Classical.choice, Quot.sound
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Nothing in Mathlib beyond the foundations.
Cited by82
Results whose statement or proof uses this declaration.
- cfc_congrproof · cited by 20
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- Real.rpow_add'proof · cited by 12
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- List.mem_dedupproof · cited by 7
- Equiv.Perm.support_mul_leproof · cited by 6
- Nat.log_eq_iffproof · cited by 5
- Complex.arg_mul_cos_add_sin_mul_Iproof · cited by 5
- Ordinal.one_lt_cof_iffproof · cited by 4
- xor_iff_or_and_not_andproof · cited by 4
- RatFunc.setOfPred_polynomial_valuation_lt_one_and_ne_zero_nonemptyproof · cited by 4
- WeierstrassCurve.Affine.nonsingular_negproof · cited by 4