Nuprl Lemma : ipolynomial-term-cons-req
∀[m:iMonomial()]. ∀[p:iMonomial() List]. ipolynomial-term([m / p]) ≡ imonomial-term(m) (+) ipolynomial-term(p)
Proof
Definitions occuring in Statement :
req_int_terms: t1 ≡ t2,
ipolynomial-term: ipolynomial-term(p),
imonomial-term: imonomial-term(m),
iMonomial: iMonomial(),
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),
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],
req_int_terms: t1 ≡ t2,
iMonomial: iMonomial(),
int_nzero: ℤ-o,
implies: P ⇒ Q,
real_term_value: real_term_value(f;t),
itermAdd: left (+) right,
int_term_ind: int_term_ind,
itermConstant: "const",
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
top: Top,
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x]
Latex:
\mforall{}[m:iMonomial()]. \mforall{}[p:iMonomial() List].
ipolynomial-term([m / p]) \mequiv{} imonomial-term(m) (+) ipolynomial-term(p)
Date html generated:
2020_05_20-AM-10_54_02
Last ObjectModification:
2020_01_02-PM-02_12_28
Theory : reals
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