Nuprl Lemma : per-or_wf
∀[A,B:Type]. (per-or(A;B) ∈ Type)
Proof
Definitions occuring in Statement :
per-or: per-or(A;B),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
per-or: per-or(A;B),
so_lambda: λ2x.t[x],
per-or-family: per-or-family(A;B),
subtype_rel: A ⊆r B,
type-function: type-function{i:l}(A),
so_apply: x[s]
Lemmas referenced :
per-exists_wf,
per-value_wf,
per-or-family_wf,
subtype_rel_self,
type-function_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
hypothesisEquality,
applyEquality,
instantiate,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A,B:Type]. (per-or(A;B) \mmember{} Type)
Date html generated:
2019_06_20-AM-11_30_32
Last ObjectModification:
2018_08_22-PM-02_07_16
Theory : per!type
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