Nuprl Lemma : Russell-theorem
¬(Type ∈ Type)
Proof
Definitions occuring in Statement :
not: ¬A,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
not: ¬A,
implies: P ⇒ Q,
false: False,
member: t ∈ T,
Russell: Russell,
isect2: T1 ⋂ T2,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
prop: ℙ
Lemmas referenced :
Russell-property,
istype-universe,
isect2_subtype_rel,
base_wf,
isect2_subtype_rel2,
istype-void,
isect2_wf,
not_wf,
equal-wf-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
thin,
voidElimination,
sqequalRule,
equalityIsType4,
universeIsType,
universeEquality,
baseClosed,
because_Cache,
dependent_set_memberEquality_alt,
isect_memberEquality,
unionElimination,
equalityElimination,
functionIsType,
isectElimination,
hypothesisEquality,
applyEquality,
instantiate,
cumulativity,
equalityTransitivity,
equalitySymmetry,
setEquality
Latex:
\mneg{}(Type \mmember{} Type)
Date html generated:
2019_10_15-AM-10_46_48
Last ObjectModification:
2018_10_09-AM-09_54_22
Theory : basic
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