Nuprl Lemma : norm-union_wf
∀[A,B:Type].
(∀[Na:id-fun(A)]. ∀[Nb:id-fun(B)]. (norm-union(Na;Nb) ∈ id-fun(A + B))) supposing (value-type(B) and value-type(A))
Proof
Definitions occuring in Statement :
norm-union: norm-union(Na;Nb),
id-fun: id-fun(T),
value-type: value-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
id-fun: id-fun(T),
norm-union: norm-union(Na;Nb),
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓
Lemmas referenced :
set_wf,
equal_wf,
value-type-has-value,
id-fun_wf,
value-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
functionExtensionality,
unionElimination,
thin,
sqequalRule,
applyEquality,
hypothesisEquality,
cumulativity,
extract_by_obid,
isectElimination,
lambdaEquality,
hypothesis,
lambdaFormation,
setElimination,
rename,
callbyvalueReduce,
independent_isectElimination,
inlEquality,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
unionEquality,
dependent_functionElimination,
independent_functionElimination,
inrEquality,
axiomEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A,B:Type].
(\mforall{}[Na:id-fun(A)]. \mforall{}[Nb:id-fun(B)]. (norm-union(Na;Nb) \mmember{} id-fun(A + B))) supposing
(value-type(B) and
value-type(A))
Date html generated:
2017_04_14-AM-07_22_09
Last ObjectModification:
2017_02_27-PM-02_55_16
Theory : call!by!value_2
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