Nuprl Lemma : not_functionality_wrt_uimplies
∀[P,Q:ℙ]. ({P supposing Q} ⇒ {¬Q supposing ¬P})
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
not: ¬A,
implies: P ⇒ Q
Definitions unfolded in proof :
not: ¬A,
guard: {T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
uimplies: b supposing a,
false: False,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
false_wf,
isect_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
independent_isectElimination,
thin,
hypothesis,
independent_functionElimination,
voidElimination,
hypothesisEquality,
lambdaEquality,
dependent_functionElimination,
because_Cache,
Error :functionIsType,
Error :universeIsType,
extract_by_obid,
isectElimination,
cumulativity,
isect_memberEquality,
functionEquality,
equalityTransitivity,
equalitySymmetry,
isectEquality,
Error :inhabitedIsType,
universeEquality
Latex:
\mforall{}[P,Q:\mBbbP{}]. (\{P supposing Q\} {}\mRightarrow{} \{\mneg{}Q supposing \mneg{}P\})
Date html generated:
2019_06_20-AM-11_14_17
Last ObjectModification:
2018_09_26-AM-10_41_52
Theory : core_2
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