Nuprl Lemma : merge-int-one-one
∀[T:Type]
∀[as,bs,cs:T List].
(as = bs ∈ (T List)) supposing
((merge-int(cs;as) = merge-int(cs;bs) ∈ (T List)) and
sorted(bs) and
sorted(as) and
sorted(cs))
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,
prop: ℙ,
and: P ∧ Q,
cand: A c∧ B,
true: True,
squash: ↓T,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
implies: P ⇒ Q
Lemmas referenced :
equal_wf,
list_wf,
merge-int_wf,
sorted_wf,
subtype_rel_wf,
merge-int-1-1,
squash_wf,
true_wf,
merge-int-comm,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
independent_isectElimination,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
intEquality,
universeEquality,
independent_pairFormation,
natural_numberEquality,
applyEquality,
lambdaEquality,
imageElimination,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]
\mforall{}[as,bs,cs:T List].
(as = bs) supposing
((merge-int(cs;as) = merge-int(cs;bs)) and
sorted(bs) and
sorted(as) and
sorted(cs))
supposing T \msubseteq{}r \mBbbZ{}
Date html generated:
2017_04_14-AM-08_49_59
Last ObjectModification:
2017_02_27-PM-03_35_25
Theory : list_0
Home
Index