Nuprl Lemma : Russell-theorem-take2
¬(Type ∈ Type)
Proof
Definitions occuring in Statement :
not: ¬A,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
not: ¬A,
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
guard: {T},
isect2: T1 ⋂ T2,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
and: P ∧ Q,
cand: A c∧ B,
squash: ↓T,
false: False
Lemmas referenced :
isect2_decomp,
bool_wf,
isect2_subtype_rel2,
isect2_subtype_rel,
not_wf,
base_wf,
isect2_wf,
equal-wf-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalRule,
cut,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
universeEquality,
baseClosed,
because_Cache,
hypothesis,
hypothesisEquality,
applyEquality,
cumulativity,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
unionElimination,
equalityElimination,
setEquality,
dependent_functionElimination,
productElimination,
independent_pairFormation,
lambdaEquality,
setElimination,
rename,
imageMemberEquality,
introduction,
imageElimination,
independent_functionElimination,
voidElimination,
dependent_set_memberEquality
Latex:
\mneg{}(Type \mmember{} Type)
Date html generated:
2016_05_15-PM-01_44_06
Last ObjectModification:
2016_01_15-PM-11_17_40
Theory : basic
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