Nuprl Lemma : mul-monomials-req
∀[m1,m2:iMonomial()]. imonomial-term(mul-monomials(m1;m2)) ≡ imonomial-term(m1) (*) imonomial-term(m2)
Proof
Definitions occuring in Statement :
req_int_terms: t1 ≡ t2,
mul-monomials: mul-monomials(m1;m2),
imonomial-term: imonomial-term(m),
iMonomial: iMonomial(),
itermMultiply: left (*) right,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iMonomial: iMonomial(),
mul-monomials: mul-monomials(m1;m2),
has-value: (a)↓,
uimplies: b supposing a,
int_nzero: ℤ-o,
req_int_terms: t1 ≡ t2,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
real_term_value: real_term_value(f;t),
itermMultiply: left (*) right,
int_term_ind: int_term_ind,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
nat: ℕ,
false: False,
ge: i ≥ j ,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
guard: {T},
or: P ∨ Q,
cons: [a / b],
le: A ≤ B,
less_than': less_than'(a;b),
colength: colength(L),
nil: [],
it: ⋅,
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),
merge-int: merge-int(as;bs),
imonomial-term: imonomial-term(m),
itermConstant: "const",
so_lambda: so_lambda4,
so_apply: x[s1;s2;s3;s4],
insert-int: insert-int(x;l),
so_lambda: so_lambda3,
so_apply: x[s1;s2;s3],
itermVar: vvar,
bool: 𝔹,
unit: Unit,
btrue: tt,
true: True,
bfalse: ff,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q
Latex:
\mforall{}[m1,m2:iMonomial()].
imonomial-term(mul-monomials(m1;m2)) \mequiv{} imonomial-term(m1) (*) imonomial-term(m2)
Date html generated:
2020_05_20-AM-10_54_32
Last ObjectModification:
2020_01_02-PM-02_10_21
Theory : reals
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