Nuprl Lemma : not_over_or
∀[A,B:ℙ]. uiff(¬(A ∨ B);(¬A) ∧ (¬B))
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
prop: ℙ,
not: ¬A,
or: P ∨ Q,
and: P ∧ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
or: P ∨ Q,
prop: ℙ,
guard: {T}
Lemmas referenced :
not_wf,
or_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
thin,
sqequalHypSubstitution,
hypothesis,
independent_functionElimination,
inlFormation,
hypothesisEquality,
voidElimination,
sqequalRule,
inrFormation,
productElimination,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
because_Cache,
Error :universeIsType,
extract_by_obid,
isectElimination,
unionElimination,
Error :productIsType,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
productEquality,
Error :inhabitedIsType,
universeEquality
Latex:
\mforall{}[A,B:\mBbbP{}]. uiff(\mneg{}(A \mvee{} B);(\mneg{}A) \mwedge{} (\mneg{}B))
Date html generated:
2019_06_20-AM-11_16_04
Last ObjectModification:
2018_09_26-AM-10_23_58
Theory : core_2
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