Nuprl Lemma : contra-cc_wf
∀[T:Type]. (CCC(T) ∈ ℙ')
Proof
Definitions occuring in Statement :
contra-cc: CCC(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
exists: ∃x:A. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
prop: ℙ,
contra-cc: CCC(T),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-universe,
subtype_rel_self,
nat_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
because_Cache,
isectElimination,
sqequalHypSubstitution,
instantiate,
thin,
applyEquality,
productEquality,
universeEquality,
hypothesisEquality,
hypothesis,
extract_by_obid,
cumulativity,
functionEquality,
sqequalRule,
cut,
introduction,
Error :isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. (CCC(T) \mmember{} \mBbbP{}')
Date html generated:
2019_06_20-PM-03_00_22
Last ObjectModification:
2019_06_12-PM-07_59_44
Theory : continuity
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