Nuprl Lemma : oal_merge_conses_lemma
∀qs,vq,kq,ps,vp,kp,b,a:Top.
([<kp, vp> / ps] ++ [<kq, vq> / qs] ~ if kq <b kp then [<kp, vp> / (ps ++ [<kq, vq> / qs])]
if kp <b kq then [<kq, vq> / ([<kp, vp> / ps] ++ qs)]
if (vp * vq) =b e then ps ++ qs
else [<kp, vp * vq> / (ps ++ qs)]
fi )
Proof
Definitions occuring in Statement :
oal_merge: ps ++ qs,
cons: [a / b],
ifthenelse: if b then t else f fi ,
top: Top,
infix_ap: x f y,
all: ∀x:A. B[x],
pair: <a, b>,
sqequal: s ~ t,
grp_id: e,
grp_op: *,
grp_eq: =b,
set_blt: a <b b
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
oal_merge: ps ++ qs,
ycomb: Y,
top: Top,
ifthenelse: if b then t else f fi ,
bfalse: ff,
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
top_wf,
null_cons_lemma,
reduce_hd_cons_lemma,
reduce_tl_cons_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}qs,vq,kq,ps,vp,kp,b,a:Top.
([<kp, vp> / ps] ++ [<kq, vq> / qs] \msim{} if kq <\msubb{} kp then [<kp, vp> / (ps ++ [<kq, vq> / qs])]
if kp <\msubb{} kq then [<kq, vq> / ([<kp, vp> / ps] ++ qs)]
if (vp * vq) =\msubb{} e then ps ++ qs
else [<kp, vp * vq> / (ps ++ qs)]
fi )
Date html generated:
2016_05_16-AM-08_17_31
Last ObjectModification:
2015_12_28-PM-06_27_09
Theory : polynom_2
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