Nuprl Lemma : merge-int-lex
∀cs,as,bs:ℤ List. ((↑as ≤_lex bs) ⇒ (↑merge-int(as;cs) ≤_lex merge-int(bs;cs)))
Proof
Definitions occuring in Statement :
intlex: l1 ≤_lex l2,
merge-int: merge-int(as;bs),
list: T List,
assert: ↑b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
uimplies: b supposing a,
so_apply: x[s],
merge-int: merge-int(as;bs),
top: Top
Lemmas referenced :
list_induction,
all_wf,
list_wf,
assert_wf,
intlex_wf,
merge-int_wf,
subtype_rel_self,
reduce_nil_lemma,
reduce_cons_lemma,
insert-int-lex
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
intEquality,
sqequalRule,
lambdaEquality,
hypothesis,
because_Cache,
functionEquality,
hypothesisEquality,
independent_isectElimination,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
rename
Latex:
\mforall{}cs,as,bs:\mBbbZ{} List. ((\muparrow{}as \mleq{}\_lex bs) {}\mRightarrow{} (\muparrow{}merge-int(as;cs) \mleq{}\_lex merge-int(bs;cs)))
Date html generated:
2016_05_14-AM-06_50_24
Last ObjectModification:
2015_12_26-PM-00_23_17
Theory : list_0
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