Nuprl Lemma : set-valueall-type
∀[A:Type]. ∀[P:A ⟶ ℙ]. valueall-type({a:A| P[a]} ) supposing valueall-type(A)
Proof
Definitions occuring in Statement :
valueall-type: valueall-type(T)
,
uimplies: b supposing a
,
uall: ∀[x:A]. B[x]
,
prop: ℙ
,
so_apply: x[s]
,
set: {x:A| B[x]}
,
function: x:A ⟶ B[x]
,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
uimplies: b supposing a
,
so_apply: x[s]
,
subtype_rel: A ⊆r B
,
valueall-type: valueall-type(T)
,
has-value: (a)↓
,
prop: ℙ
Lemmas referenced :
subtype-valueall-type,
equal-wf-base,
base_wf,
valueall-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setEquality,
hypothesisEquality,
applyEquality,
hypothesis,
because_Cache,
sqequalRule,
independent_isectElimination,
lambdaEquality,
setElimination,
rename,
isect_memberEquality,
axiomSqleEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbP{}]. valueall-type(\{a:A| P[a]\} ) supposing valueall-type(A)
Date html generated:
2016_05_13-PM-03_27_00
Last ObjectModification:
2015_12_26-AM-09_28_07
Theory : call!by!value_1
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