Nuprl Lemma : not_functionality_wrt_implies
∀[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},
not: ¬A,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Definitions unfolded in proof :
not: ¬A,
guard: {T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
implies: P ⇒ Q,
false: False,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
false_wf,
rev_implies_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
introduction,
cut,
lambdaFormation,
hypothesis,
hypothesisEquality,
functionEquality,
extract_by_obid,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
because_Cache,
cumulativity,
Error :functionIsType,
Error :universeIsType,
isect_memberEquality,
isectElimination,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
voidElimination,
universeEquality,
independent_functionElimination
Latex:
\mforall{}[P,Q:\mBbbP{}]. \{(\mneg{}P) {}\mRightarrow{} (\mneg{}Q)\} supposing \{P \mLeftarrow{}{} Q\}
Date html generated:
2019_06_20-AM-11_17_08
Last ObjectModification:
2018_09_26-AM-10_24_39
Theory : core_2
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