Nuprl Lemma : union-valueall-type
∀[A,B:Type]. (valueall-type(A) ⇒ valueall-type(B) ⇒ valueall-type(A + B))
Proof
Definitions occuring in Statement :
valueall-type: valueall-type(T),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
valueall-type: valueall-type(T),
uimplies: b supposing a,
sq_stable: SqStable(P),
all: ∀x:A. B[x],
top: Top,
has-value: (a)↓,
has-valueall: has-valueall(a),
prop: ℙ,
squash: ↓T
Lemmas referenced :
sq_stable__has-value,
evalall-inl,
valueall-type-has-valueall,
has-value_wf_base,
is-exception_wf,
evalall-inr,
equal_wf,
equal-wf-base,
base_wf,
valueall-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
hypothesis,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
because_Cache,
unionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
callbyvalueReduce,
independent_isectElimination,
divergentSqle,
sqleReflexivity,
dependent_functionElimination,
imageMemberEquality,
imageElimination,
unionEquality,
cumulativity,
lambdaEquality,
axiomSqleEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. (valueall-type(A) {}\mRightarrow{} valueall-type(B) {}\mRightarrow{} valueall-type(A + B))
Date html generated:
2017_04_14-AM-07_14_58
Last ObjectModification:
2017_02_27-PM-02_50_37
Theory : call!by!value_1
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