Nuprl Lemma : ipolynomial-term-cons
∀[m:iMonomial()]. ∀[p:iMonomial() List]. ipolynomial-term([m / p]) ≡ imonomial-term(m) "+" ipolynomial-term(p)
Proof
Definitions occuring in Statement :
ipolynomial-term: ipolynomial-term(p),
imonomial-term: imonomial-term(m),
iMonomial: iMonomial(),
equiv_int_terms: t1 ≡ t2,
itermAdd: left "+" right,
cons: [a / b],
list: T List,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
or: P ∨ Q,
ipolynomial-term: ipolynomial-term(p),
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
cons: [a / b],
equiv_int_terms: t1 ≡ t2,
int_term_value: int_term_value(f;t),
itermAdd: left "+" right,
int_term_ind: int_term_ind,
itermConstant: "const",
subtype_rel: A ⊆r B,
iMonomial: iMonomial(),
so_lambda: λ2x.t[x],
uimplies: b supposing a,
prop: ℙ,
so_apply: x[s],
int_nzero: ℤ-o,
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
iMonomial_wf,
list-cases,
null_cons_lemma,
spread_cons_lemma,
null_nil_lemma,
list_accum_nil_lemma,
product_subtype_list,
list_accum_cons_lemma,
list_wf,
add-zero,
int_term_value_wf,
imonomial-term_wf,
subtype_rel_product,
int_nzero_wf,
sorted_wf,
subtype_rel_self,
itermAdd_wf,
equiv_int_terms_weakening,
list_induction,
all_wf,
int_term_wf,
equiv_int_terms_wf,
list_accum_wf,
subtype_rel_list,
equiv_int_terms_functionality,
itermAdd_functionality,
add-associates,
add-commutes
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
unionElimination,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
promote_hyp,
hypothesis_subsumption,
productElimination,
lambdaEquality,
axiomEquality,
functionEquality,
intEquality,
because_Cache,
lambdaFormation,
applyEquality,
setEquality,
independent_isectElimination,
setElimination,
rename,
independent_pairEquality,
independent_functionElimination,
productEquality,
addEquality
Latex:
\mforall{}[m:iMonomial()]. \mforall{}[p:iMonomial() List].
ipolynomial-term([m / p]) \mequiv{} imonomial-term(m) "+" ipolynomial-term(p)
Date html generated:
2016_05_14-AM-07_00_57
Last ObjectModification:
2015_12_26-PM-01_11_56
Theory : omega
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