Nuprl Lemma : add-poly-prepend-sq
∀[p,q,l:iMonomial() List]. (add-ipoly-prepend(p;q;l) ~ rev(l) + add-ipoly(p;q))
Proof
Definitions occuring in Statement :
add-ipoly-prepend: add-ipoly-prepend(p;q;l),
add-ipoly: add-ipoly(p;q),
iMonomial: iMonomial(),
rev-append: rev(as) + bs,
list: T List,
uall: ∀[x:A]. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
iMonomial: iMonomial(),
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
int_nzero: ℤ-o,
all: ∀x:A. B[x]
Lemmas referenced :
add-poly-prepend-sq1,
subtype_rel_list,
list_wf,
subtype_rel_product,
int_nzero_wf,
sorted_wf,
subtype_rel_self,
iMonomial_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
because_Cache,
productEquality,
intEquality,
hypothesis,
independent_isectElimination,
sqequalRule,
lambdaEquality,
setEquality,
setElimination,
rename,
lambdaFormation
Latex:
\mforall{}[p,q,l:iMonomial() List]. (add-ipoly-prepend(p;q;l) \msim{} rev(l) + add-ipoly(p;q))
Date html generated:
2017_09_29-PM-05_53_01
Last ObjectModification:
2017_05_11-PM-06_37_37
Theory : omega
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