Nuprl Lemma : per-function-type-apply
∀[A:Type]. ∀[B:type-function{i:l}(A)]. ∀[a:A]. (B[a] ∈ Type)
Proof
Definitions occuring in Statement :
type-function: type-function{i:l}(A),
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_apply: x[s]
Lemmas referenced :
apply_wf_type-function,
type-function_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:type-function\{i:l\}(A)]. \mforall{}[a:A]. (B[a] \mmember{} Type)
Date html generated:
2016_05_13-PM-03_53_47
Last ObjectModification:
2015_12_26-AM-10_40_59
Theory : per!type
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