Nuprl Lemma : rat_term_to_ipolys_wf
∀[t:rat_term()]. (rat_term_to_ipolys(t) ∈ iPolynomial() × iPolynomial())
Proof
Definitions occuring in Statement :
rat_term_to_ipolys: rat_term_to_ipolys(t),
rat_term: rat_term(),
iPolynomial: iPolynomial(),
uall: ∀[x:A]. B[x],
member: t ∈ T,
product: x:A × B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
iMonomial: iMonomial(),
member: t ∈ T,
int_nzero: ℤ-o,
true: True,
nequal: a ≠ b ∈ T ,
not: ¬A,
implies: P ⇒ Q,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
false: False,
prop: ℙ,
sorted: sorted(L),
select: L[n],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than: a < b,
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
iPolynomial: iPolynomial(),
rat_term_to_ipolys: rat_term_to_ipolys(t),
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4]
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
istype-int,
nequal_wf,
nil_wf,
stuck-spread,
istype-base,
istype-void,
length_of_nil_lemma,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformless_wf,
itermVar_wf,
intformle_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
intformnot_wf,
int_formula_prop_not_lemma,
int_seg_wf,
sorted_wf,
cons_wf,
iMonomial_wf,
length_of_cons_lemma,
length_wf,
imonomial-less_wf,
select_wf,
decidable__lt,
rat_term_wf,
add_ipoly_wf,
mul_ipoly_wf,
minus-poly_wf,
rat_term_ind_wf_simple,
iPolynomial_wf,
decidable__equal_int,
le_weakening2,
itermAdd_wf,
int_term_value_add_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
independent_pairEquality,
dependent_set_memberEquality_alt,
natural_numberEquality,
lambdaFormation_alt,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
hypothesis,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
equalityIstype,
baseClosed,
sqequalBase,
universeIsType,
hypothesisEquality,
sqequalRule,
isect_memberEquality_alt,
setElimination,
rename,
productElimination,
imageElimination,
approximateComputation,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
independent_pairFormation,
because_Cache,
unionElimination,
functionIsType,
inhabitedIsType,
productIsType,
productEquality,
int_eqReduceFalseSq,
closedConclusion
Latex:
\mforall{}[t:rat\_term()]. (rat\_term\_to\_ipolys(t) \mmember{} iPolynomial() \mtimes{} iPolynomial())
Date html generated:
2019_10_29-AM-09_31_27
Last ObjectModification:
2019_04_01-AM-10_43_51
Theory : reals
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