Nuprl Lemma : base-type-family-implies
∀[A:Type]. ∀[B:Base]. ∀a:A. (B[a] ∈ Type) supposing base-type-family{i:l}(A;a.B[a])
Proof
Definitions occuring in Statement :
base-type-family: base-type-family{i:l}(A;a.B[a]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
member: t ∈ T,
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
label: ...$L... t,
so_apply: x[s],
base-type-family: base-type-family{i:l}(A;a.B[a]),
squash: ↓T,
true: True
Lemmas referenced :
true_wf,
squash_wf,
member_wf,
base_wf,
base-type-family_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
pointwiseFunctionality,
sqequalHypSubstitution,
hypothesis,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
thin,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
lemma_by_obid,
isectElimination,
cumulativity,
baseApply,
closedConclusion,
baseClosed,
isect_memberEquality,
universeEquality,
independent_isectElimination,
applyEquality,
instantiate,
imageElimination,
natural_numberEquality,
imageMemberEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:Base]. \mforall{}a:A. (B[a] \mmember{} Type) supposing base-type-family\{i:l\}(A;a.B[a])
Date html generated:
2016_05_13-PM-03_53_28
Last ObjectModification:
2016_01_14-PM-07_15_55
Theory : per!type
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