Nuprl Lemma : type-function_wf
∀[A:Type]. (type-function{i:l}(A) ∈ 𝕌')
Proof
Definitions occuring in Statement :
type-function: type-function{i:l}(A),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
type-function: type-function{i:l}(A),
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
base-type-family: base-type-family{i:l}(A;a.B[a]),
prop: ℙ
Lemmas referenced :
base_wf,
equal-wf-base,
per-function_wf_base_family
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
hypothesisEquality,
sqequalRule,
baseClosed,
independent_isectElimination,
universeEquality,
hypothesis,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache
Latex:
\mforall{}[A:Type]. (type-function\{i:l\}(A) \mmember{} \mBbbU{}')
Date html generated:
2016_05_13-PM-03_53_39
Last ObjectModification:
2016_01_14-PM-07_15_47
Theory : per!type
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