Nuprl Lemma : per-class_wf
∀[T:Type]. ∀[a:Base ⋃ T]. (per-class(T;a) ∈ Type)
Proof
Definitions occuring in Statement :
per-class: per-class(T;a),
b-union: A ⋃ B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
per-class: per-class(T;a),
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
bool: 𝔹,
unit: Unit,
ifthenelse: if b then t else f fi ,
pi2: snd(t),
prop: ℙ
Lemmas referenced :
b-union_wf,
base_wf,
equal-wf-base,
equal-wf-base-T
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
setEquality,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
because_Cache,
universeEquality,
imageElimination,
productElimination,
unionElimination,
equalityElimination
Latex:
\mforall{}[T:Type]. \mforall{}[a:Base \mcup{} T]. (per-class(T;a) \mmember{} Type)
Date html generated:
2016_05_13-PM-04_12_30
Last ObjectModification:
2015_12_26-AM-11_12_07
Theory : subtype_1
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