Nuprl Lemma : mul-mono-poly-req
∀[m:iMonomial()]. ∀[p:iMonomial() List].
ipolynomial-term(mul-mono-poly(m;p)) ≡ imonomial-term(m) (*) ipolynomial-term(p)
Proof
Definitions occuring in Statement :
req_int_terms: t1 ≡ t2,
mul-mono-poly: mul-mono-poly(m;p),
ipolynomial-term: ipolynomial-term(p),
imonomial-term: imonomial-term(m),
iMonomial: iMonomial(),
itermMultiply: left (*) right,
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],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
and: P ∧ Q,
prop: ℙ,
req_int_terms: t1 ≡ t2,
guard: {T},
or: P ∨ Q,
mul-mono-poly: mul-mono-poly(m;p),
so_lambda: so_lambda3,
so_apply: x[s1;s2;s3],
cons: [a / b],
le: A ≤ B,
less_than': less_than'(a;b),
iMonomial: iMonomial(),
int_nzero: ℤ-o,
colength: colength(L),
nil: [],
it: ⋅,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
decidable: Dec(P),
subtype_rel: A ⊆r B,
has-value: (a)↓,
itermMultiply: left (*) right,
int_term_ind: int_term_ind,
itermConstant: "const",
real_term_value: real_term_value(f;t),
btrue: tt,
ifthenelse: if b then t else f fi ,
ipolynomial-term: ipolynomial-term(p),
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
itermAdd: left (+) right,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[m:iMonomial()]. \mforall{}[p:iMonomial() List].
ipolynomial-term(mul-mono-poly(m;p)) \mequiv{} imonomial-term(m) (*) ipolynomial-term(p)
Date html generated:
2020_05_20-AM-10_54_39
Last ObjectModification:
2019_12_14-PM-00_53_43
Theory : reals
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