Nuprl Lemma : merge-int-1-1
∀[T:Type]
∀[cs,as,bs:T List].
(as = bs ∈ (T List)) supposing ((merge-int(as;cs) = merge-int(bs;cs) ∈ (T List)) and sorted(bs) and sorted(as))
supposing T ⊆r ℤ
Proof
Definitions occuring in Statement :
sorted: sorted(L),
merge-int: merge-int(as;bs),
list: T List,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
merge-int: merge-int(as;bs),
all: ∀x:A. B[x],
top: Top,
guard: {T}
Lemmas referenced :
list_induction,
uall_wf,
list_wf,
isect_wf,
sorted_wf,
equal_wf,
merge-int_wf,
reduce_nil_lemma,
reduce_cons_lemma,
insert-int_wf,
subtype_rel_wf,
insert-int-1-1,
merge-int-sorted
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
cumulativity,
hypothesis,
because_Cache,
independent_isectElimination,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
rename,
intEquality,
universeEquality
Latex:
\mforall{}[T:Type]
\mforall{}[cs,as,bs:T List].
(as = bs) supposing ((merge-int(as;cs) = merge-int(bs;cs)) and sorted(bs) and sorted(as))
supposing T \msubseteq{}r \mBbbZ{}
Date html generated:
2017_04_14-AM-08_49_48
Last ObjectModification:
2017_02_27-PM-03_35_39
Theory : list_0
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