Nuprl Lemma : function-value-type
∀[A:Type]. ∀[B:A ⟶ Type]. value-type(a:A ⟶ B[a]) supposing ↓∃a:A. value-type(B[a])
Proof
Definitions occuring in Statement :
value-type: value-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
exists: ∃x:A. B[x],
squash: ↓T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
squash: ↓T,
so_apply: x[s],
sq_stable: SqStable(P),
implies: P ⇒ Q,
exists: ∃x:A. B[x],
value-type: value-type(T),
has-value: (a)↓,
prop: ℙ,
so_lambda: λ2x.t[x]
Lemmas referenced :
value-type_wf,
exists_wf,
squash_wf,
base_wf,
equal-wf-base,
value-type-has-value,
sq_stable__value-type
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
imageElimination,
lemma_by_obid,
isectElimination,
thin,
functionEquality,
hypothesisEquality,
applyEquality,
hypothesis,
independent_functionElimination,
productElimination,
rename,
independent_isectElimination,
callbyvalueApply,
sqequalRule,
axiomSqleEquality,
because_Cache,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
baseClosed,
lambdaEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. value-type(a:A {}\mrightarrow{} B[a]) supposing \mdownarrow{}\mexists{}a:A. value-type(B[a])
Date html generated:
2016_05_13-PM-03_26_43
Last ObjectModification:
2016_01_14-PM-06_44_09
Theory : call!by!value_1
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