Nuprl Lemma : rP_to_poly-int_term_to_rP
∀[t:int_term()]. ∀[s:iPolynomial() List]. (rP_to_poly(s;int_term_to_rP(t)) ~ [int_term_to_ipoly(t) / s])
Proof
Definitions occuring in Statement :
rP_to_poly: rP_to_poly(stack;L),
int_term_to_rP: int_term_to_rP(t),
int_term_to_ipoly: int_term_to_ipoly(t),
iPolynomial: iPolynomial(),
int_term: int_term(),
cons: [a / b],
list: T List,
uall: ∀[x:A]. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
and: P ∧ Q,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
iPolynomial: iPolynomial(),
so_lambda: λ2x.t[x],
int_seg: {i..j-},
sq_stable: SqStable(P),
implies: P ⇒ Q,
lelt: i ≤ j < k,
squash: ↓T,
guard: {T},
all: ∀x:A. B[x],
so_apply: x[s],
iMonomial: iMonomial(),
prop: ℙ,
int_nzero: ℤ-o,
subtype_rel: A ⊆r B,
int_term_to_ipoly: int_term_to_ipoly(t),
int_term_to_rP: int_term_to_rP(t),
itermConstant: "const",
int_term_ind: int_term_ind,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
rP_to_poly: rP_to_poly(stack;L),
cons: [a / b],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
itermVar: vvar,
itermAdd: left (+) right,
itermSubtract: left (-) right,
itermMultiply: left (*) right,
itermMinus: "-"num,
list_ind: list_ind,
spreadn: spread3,
nil: [],
it: ⋅
Lemmas referenced :
int_term_subtype_base,
list_subtype_base,
iPolynomial_wf,
set_subtype_base,
list_wf,
iMonomial_wf,
all_wf,
int_seg_wf,
length_wf,
imonomial-less_wf,
select_wf,
sq_stable__le,
less_than_transitivity2,
le_weakening2,
product_subtype_base,
int_nzero_wf,
sorted_wf,
subtype_rel_self,
nequal_wf,
int_subtype_base,
int_term_wf,
int_term-induction,
sqequal-wf-base,
list_ind_cons_lemma,
list_ind_nil_lemma,
spread_cons_lemma,
eager-append-is-append,
int_term_to_rP_wf,
subtype_rel_list,
top_wf,
cons_wf,
nil_wf,
append_assoc,
append_wf,
eager-append_wf,
int_term_to_ipoly_wf,
append_back_nil
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
introduction,
extract_by_obid,
hypothesis,
independent_pairFormation,
sqequalHypSubstitution,
isectElimination,
thin,
independent_isectElimination,
sqequalRule,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
because_Cache,
setElimination,
rename,
independent_functionElimination,
productElimination,
imageMemberEquality,
baseClosed,
imageElimination,
dependent_functionElimination,
setEquality,
intEquality,
lambdaFormation,
isect_memberFormation,
sqequalAxiom,
baseApply,
closedConclusion,
applyEquality,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[t:int\_term()]. \mforall{}[s:iPolynomial() List].
(rP\_to\_poly(s;int\_term\_to\_rP(t)) \msim{} [int\_term\_to\_ipoly(t) / s])
Date html generated:
2017_09_29-PM-05_54_46
Last ObjectModification:
2017_05_12-PM-11_39_17
Theory : omega
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