Nuprl Lemma : ipolynomial-term_wf
∀[p:iMonomial() List]. (ipolynomial-term(p) ∈ int_term())
Proof
Definitions occuring in Statement :
ipolynomial-term: ipolynomial-term(p),
iMonomial: iMonomial(),
int_term: int_term(),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ipolynomial-term: ipolynomial-term(p),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
not: ¬A,
prop: ℙ,
rev_implies: P ⇐ Q,
false: False,
or: P ∨ Q,
nil: [],
cons: [a / b],
subtype_rel: A ⊆r B,
iMonomial: iMonomial(),
so_lambda: λ2x.t[x],
so_apply: x[s],
int_nzero: ℤ-o,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
null_wf,
iMonomial_wf,
bool_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
list_wf,
eqtt_to_assert,
assert_of_null,
itermConstant_wf,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
list-cases,
it_wf,
unit_wf2,
nil_wf,
equal_wf,
product_subtype_list,
list_accum_wf,
int_term_wf,
subtype_rel_list,
subtype_rel_product,
int_nzero_wf,
sorted_wf,
subtype_rel_self,
imonomial-term_wf,
itermAdd_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
baseClosed,
independent_functionElimination,
because_Cache,
productElimination,
independent_isectElimination,
natural_numberEquality,
independent_pairFormation,
impliesFunctionality,
voidElimination,
dependent_functionElimination,
promote_hyp,
hypothesis_subsumption,
productEquality,
intEquality,
applyEquality,
lambdaEquality,
setEquality,
setElimination,
rename,
independent_pairEquality,
axiomEquality
Latex:
\mforall{}[p:iMonomial() List]. (ipolynomial-term(p) \mmember{} int\_term())
Date html generated:
2017_04_14-AM-08_58_00
Last ObjectModification:
2017_02_27-PM-03_41_02
Theory : omega
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