Nuprl Lemma : not_functionality_wrt_uiff
∀[P,Q:ℙ]. ({uiff(P;Q)} ⇒ {uiff(¬P;¬Q)})
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
not: ¬A,
implies: P ⇒ Q
Definitions unfolded in proof :
guard: {T},
not: ¬A,
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
false: False,
prop: ℙ
Lemmas referenced :
false_wf,
uiff_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
independent_isectElimination,
hypothesis,
independent_functionElimination,
voidElimination,
hypothesisEquality,
lambdaEquality,
dependent_functionElimination,
Error :functionIsType,
Error :universeIsType,
extract_by_obid,
because_Cache,
isectElimination,
independent_pairEquality,
isect_memberEquality,
functionEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
universeEquality
Latex:
\mforall{}[P,Q:\mBbbP{}]. (\{uiff(P;Q)\} {}\mRightarrow{} \{uiff(\mneg{}P;\mneg{}Q)\})
Date html generated:
2019_06_20-AM-11_14_19
Last ObjectModification:
2018_09_26-AM-10_41_51
Theory : core_2
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