Nuprl Lemma : minus-poly-req
∀p:iPolynomial(). ipolynomial-term(minus-poly(p)) ≡ "-"ipolynomial-term(p)
Proof
Definitions occuring in Statement :
req_int_terms: t1 ≡ t2,
minus-poly: minus-poly(p),
ipolynomial-term: ipolynomial-term(p),
iPolynomial: iPolynomial(),
itermMinus: "-"num,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
iPolynomial: iPolynomial(),
member: t ∈ T,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
req_int_terms: t1 ≡ t2,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
uimplies: b supposing a,
less_than: a < b,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
prop: ℙ,
subtype_rel: A ⊆r B,
so_apply: x[s],
nat: ℕ,
ge: i ≥ j ,
guard: {T},
cons: [a / b],
less_than': less_than'(a;b),
colength: colength(L),
nil: [],
it: ⋅,
sq_type: SQType(T),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uiff: uiff(P;Q),
ipolynomial-term: ipolynomial-term(p),
minus-poly: minus-poly(p),
ifthenelse: if b then t else f fi ,
btrue: tt,
real_term_value: real_term_value(f;t),
itermConstant: "const",
int_term_ind: int_term_ind,
itermMinus: "-"num,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtract: n - m,
bool: 𝔹,
unit: Unit,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
iMonomial: iMonomial(),
int_nzero: ℤ-o,
rev_uimplies: rev_uimplies(P;Q),
minus-monomial: minus-monomial(m),
itermAdd: left (+) right
Latex:
\mforall{}p:iPolynomial(). ipolynomial-term(minus-poly(p)) \mequiv{} "-"ipolynomial-term(p)
Date html generated:
2020_05_20-AM-10_54_22
Last ObjectModification:
2020_01_02-PM-02_12_00
Theory : reals
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