### 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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