Nuprl Lemma : not_functionality_wrt_iff
∀[P,Q:ℙ]. {¬P ⇐⇒ ¬Q} supposing P ⇐⇒ Q
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
iff: P ⇐⇒ Q,
not: ¬A
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
not: ¬A,
false: False,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
not_wf,
iff_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
lambdaFormation,
hypothesisEquality,
hypothesis,
independent_functionElimination,
voidElimination,
extract_by_obid,
isectElimination,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
because_Cache,
Error :productIsType,
Error :functionIsType,
Error :universeIsType,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
universeEquality
Latex:
\mforall{}[P,Q:\mBbbP{}]. \{\mneg{}P \mLeftarrow{}{}\mRightarrow{} \mneg{}Q\} supposing P \mLeftarrow{}{}\mRightarrow{} Q
Date html generated:
2019_06_20-AM-11_17_05
Last ObjectModification:
2018_09_26-AM-10_24_37
Theory : core_2
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