Nuprl Lemma : Russell-paradox
¬(𝕌' ⊆r Type)
Proof
Definitions occuring in Statement :
subtype_rel: A ⊆r B,
not: ¬A,
universe: Type
Definitions unfolded in proof :
not: ¬A,
implies: P ⇒ Q,
false: False,
member: t ∈ T,
uall: ∀[x:A]. B[x],
Russell: Russell,
isect2: T1 ⋂ T2,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
Russell-property,
subtype_rel_wf,
bool_wf,
Russell_wf,
isect2_subtype_rel2,
base_wf,
not_wf,
equal-wf-base,
isect2_subtype_rel
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
independent_functionElimination,
thin,
voidElimination,
universeIsType,
instantiate,
isectElimination,
universeEquality,
cumulativity,
hypothesis,
dependent_set_memberEquality_alt,
isect_memberEquality,
unionElimination,
equalityElimination,
sqequalRule,
applyEquality,
baseClosed,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache
Latex:
\mneg{}(\mBbbU{}' \msubseteq{}r Type)
Date html generated:
2019_10_15-AM-10_46_46
Last ObjectModification:
2018_10_09-AM-09_38_28
Theory : basic
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