Nuprl Lemma : val-union-l-union
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[as,bs:T List]. val-union(eq;as;bs) ~ as ⋃ bs supposing valueall-type(T)
Proof
Definitions occuring in Statement :
val-union: val-union(eq;as;bs),
l-union: as ⋃ bs,
list: T List,
deq: EqDecider(T),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
l-union: as ⋃ bs,
val-union: val-union(eq;as;bs),
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a)
Lemmas referenced :
valueall-type-has-valueall,
list_wf,
list-valueall-type,
evalall-reduce,
valueall-type_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
callbyvalueReduce,
because_Cache,
sqequalAxiom,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[as,bs:T List].
val-union(eq;as;bs) \msim{} as \mcup{} bs supposing valueall-type(T)
Date html generated:
2016_05_14-PM-03_25_20
Last ObjectModification:
2015_12_26-PM-06_22_26
Theory : decidable!equality
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