Nuprl Lemma : member-not
∀[A:ℙ]. ∀[z:Top]. λx.z ∈ ¬A supposing ¬A
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
prop: ℙ,
not: ¬A,
member: t ∈ T,
lambda: λx.A[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
member: t ∈ T,
false: False,
prop: ℙ
Lemmas referenced :
istype-void,
istype-top
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
Error :lambdaEquality_alt,
sqequalHypSubstitution,
independent_functionElimination,
thin,
hypothesis,
voidElimination,
Error :universeIsType,
because_Cache,
sqequalRule,
Error :functionIsType,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
universeEquality
Latex:
\mforall{}[A:\mBbbP{}]. \mforall{}[z:Top]. \mlambda{}x.z \mmember{} \mneg{}A supposing \mneg{}A
Date html generated:
2019_06_20-AM-11_14_29
Last ObjectModification:
2018_10_27-PM-05_04_44
Theory : core_2
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