Nuprl Lemma : set-value-type
∀[A:Type]. ∀[P:A ⟶ ℙ]. value-type({a:A| P[a]} ) supposing value-type(A)
Proof
Definitions occuring in Statement :
value-type: value-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,
value-type: value-type(T),
has-value: (a)↓,
prop: ℙ
Lemmas referenced :
subtype-value-type,
equal-wf-base,
base_wf,
value-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{}]. value-type(\{a:A| P[a]\} ) supposing value-type(A)
Date html generated:
2016_05_13-PM-03_27_03
Last ObjectModification:
2015_12_26-AM-09_28_04
Theory : call!by!value_1
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