Nuprl Lemma : int_term_to_ipoly_wf
∀[t:int_term()]. (int_term_to_ipoly(t) ∈ iPolynomial())
Proof
Definitions occuring in Statement :
int_term_to_ipoly: int_term_to_ipoly(t),
iPolynomial: iPolynomial(),
int_term: int_term(),
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_term_to_ipoly: int_term_to_ipoly(t),
so_lambda: λ2x.t[x],
iPolynomial: iPolynomial(),
all: ∀x:A. B[x],
int_seg: {i..j-},
uimplies: b supposing a,
sq_stable: SqStable(P),
implies: P ⇒ Q,
lelt: i ≤ j < k,
and: P ∧ Q,
squash: ↓T,
guard: {T},
so_apply: x[s],
prop: ℙ,
false: False,
not: ¬A,
iMonomial: iMonomial(),
int_nzero: ℤ-o,
nequal: a ≠ b ∈ T ,
sorted: sorted(L),
exists: ∃x:A. B[x],
top: Top,
true: True,
sq_type: SQType(T),
uiff: uiff(P;Q),
subtract: n - m,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
or: P ∨ Q,
nat_plus: ℕ+,
less_than: a < b
Lemmas referenced :
int_term_ind_wf_simple,
iPolynomial_wf,
nil_wf,
iMonomial_wf,
length_of_nil_lemma,
int_seg_wf,
length_wf,
all_wf,
imonomial-less_wf,
select_wf,
sq_stable__le,
less_than_transitivity2,
le_weakening2,
cons_wf,
nequal_wf,
less_than_transitivity1,
less_than_irreflexivity,
equal_wf,
sorted_wf,
subtype_rel_self,
length_of_cons_lemma,
list_wf,
subtype_base_sq,
int_subtype_base,
equal-wf-base,
true_wf,
less-iff-le,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-associates,
zero-add,
add_functionality_wrt_le,
add-commutes,
le-add-cancel2,
add_ipoly_wf,
int_term_wf,
minus-poly_wf,
mul_ipoly_wf,
subtract_wf,
minus-zero,
add-zero,
not-equal-implies-less,
one-mul,
add-mul-special,
two-mul,
mul-distributes-right,
zero-mul,
omega-shadow,
le_reflexive,
false_wf,
less_than_wf,
mul-distributes,
mul-associates,
mul-commutes,
int_seg_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
lambdaEquality,
int_eqEquality,
natural_numberEquality,
dependent_set_memberEquality,
lambdaFormation,
setElimination,
rename,
voidEquality,
because_Cache,
independent_isectElimination,
independent_functionElimination,
productElimination,
imageMemberEquality,
baseClosed,
imageElimination,
dependent_functionElimination,
independent_pairEquality,
intEquality,
voidElimination,
dependent_pairFormation,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
isect_memberEquality,
productEquality,
addLevel,
instantiate,
cumulativity,
addEquality,
applyEquality,
minusEquality,
sqequalIntensionalEquality,
axiomEquality,
unionElimination,
multiplyEquality,
independent_pairFormation
Latex:
\mforall{}[t:int\_term()]. (int\_term\_to\_ipoly(t) \mmember{} iPolynomial())
Date html generated:
2017_09_29-PM-05_54_36
Last ObjectModification:
2017_07_26-PM-01_42_59
Theory : omega
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