Nuprl Lemma : extend-type_wf
∀[T:Type]. ((T)+ ∈ Type)
Proof
Definitions occuring in Statement :
extend-type: (T)+,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
extend-type: (T)+,
so_lambda: λ2x y.t[x; y],
prop: ℙ,
and: P ∧ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
so_apply: x[s1;s2],
uimplies: b supposing a
Lemmas referenced :
quotient_wf,
base_wf,
iff_wf,
equal-wf-base,
equal-wf-T-base,
istype-base,
extend-type-equiv,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
Error :lambdaEquality_alt,
productEquality,
because_Cache,
functionEquality,
Error :inhabitedIsType,
hypothesisEquality,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]. ((T)+ \mmember{} Type)
Date html generated:
2019_06_20-PM-00_33_24
Last ObjectModification:
2018_11_25-PM-06_36_45
Theory : quot_1
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