Nuprl Lemma : merge_wf
∀[T:Type]. ∀[as,bs:T List]. (merge(as;bs) ∈ T List) supposing T ⊆r ℤ
Proof
Definitions occuring in Statement :
merge: merge(as;bs),
list: T List,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
merge: merge(as;bs)
Lemmas referenced :
reduce_wf,
list_wf,
s-insert_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
intEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[as,bs:T List]. (merge(as;bs) \mmember{} T List) supposing T \msubseteq{}r \mBbbZ{}
Date html generated:
2016_05_15-PM-03_52_25
Last ObjectModification:
2015_12_27-PM-01_23_29
Theory : general
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