Nuprl Lemma : rat_term_polynomial
∀r:rat_term(). let p,q = rat_term_to_ipolys(r) in r ≡ ipolynomial-term(p)/ipolynomial-term(q)
Proof
Definitions occuring in Statement :
req_rat_term: r ≡ p/q,
rat_term_to_ipolys: rat_term_to_ipolys(t),
rat_term: rat_term(),
ipolynomial-term: ipolynomial-term(p),
all: ∀x:A. B[x],
spread: spread def
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
iPolynomial: iPolynomial(),
so_apply: x[s],
rat_term_to_ipolys: rat_term_to_ipolys(t),
rat_term_ind: rat_term_ind,
rtermConstant: "const",
rtermVar: rtermVar(var),
rtermAdd: left "+" right,
req_rat_term: r ≡ p/q,
rat_term_to_real: rat_term_to_real(f;t),
and: P ∧ Q,
cand: A c∧ B,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
rtermSubtract: left "-" right,
rtermMultiply: left "*" right,
rtermDivide: num "/" denom,
rtermMinus: rtermMinus(num),
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
sq_type: SQType(T),
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,
imonomial-term: imonomial-term(m),
rneq: x ≠ y,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
false: False,
not: ¬A,
rdiv: (x/y),
req_int_terms: t1 ≡ t2,
real_term_value: real_term_value(f;t),
itermAdd: left (+) right,
int_term_ind: int_term_ind,
itermMultiply: left (*) right,
itermMinus: "-"num,
exists: ∃x:A. B[x],
istype: istype(T)
Latex:
\mforall{}r:rat\_term(). let p,q = rat\_term\_to\_ipolys(r) in r \mequiv{} ipolynomial-term(p)/ipolynomial-term(q)
Date html generated:
2020_05_20-AM-10_59_50
Last ObjectModification:
2020_01_06-PM-00_28_23
Theory : reals
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