Nuprl Lemma : isect-value-type
∀[A:Type]. ∀[B:A ⟶ Type]. ((∃a:A. value-type(B[a])) ⇒ value-type(⋂a:A. B[a]))
Proof
Definitions occuring in Statement :
value-type: value-type(T),
uall: ∀[x:A]. B[x],
so_apply: x[s],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
so_apply: x[s],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
value-type: value-type(T),
has-value: (a)↓
Lemmas referenced :
subtype-value-type,
exists_wf,
value-type_wf,
equal-wf-base,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
lemma_by_obid,
isectElimination,
isectEquality,
hypothesisEquality,
applyEquality,
independent_isectElimination,
sqequalRule,
lambdaEquality,
equalityTransitivity,
equalitySymmetry,
hypothesis,
dependent_functionElimination,
isect_memberEquality,
axiomSqleEquality,
because_Cache,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. ((\mexists{}a:A. value-type(B[a])) {}\mRightarrow{} value-type(\mcap{}a:A. B[a]))
Date html generated:
2016_05_13-PM-03_27_08
Last ObjectModification:
2015_12_26-AM-09_28_02
Theory : call!by!value_1
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