Nuprl Lemma : rpolynomial_functionality
∀[n:ℕ]. ∀[a,b:ℕn + 1 ⟶ ℝ]. ∀[x,y:ℝ].
((Σi≤n. a_i * x^i) = (Σi≤n. b_i * y^i)) supposing ((x = y) and a[k] = b[k] for k ∈ [0,n])
Proof
Definitions occuring in Statement :
pointwise-req: x[k] = y[k] for k ∈ [n,m],
rpolynomial: (Σi≤n. a_i * x^i),
req: x = y,
real: ℝ,
int_seg: {i..j-},
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
rpolynomial: (Σi≤n. a_i * x^i),
nat: ℕ,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than: a < b,
squash: ↓T,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
prop: ℙ,
so_apply: x[s],
pointwise-req: x[k] = y[k] for k ∈ [n,m],
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[a,b:\mBbbN{}n + 1 {}\mrightarrow{} \mBbbR{}]. \mforall{}[x,y:\mBbbR{}].
((\mSigma{}i\mleq{}n. a\_i * x\^{}i) = (\mSigma{}i\mleq{}n. b\_i * y\^{}i)) supposing ((x = y) and a[k] = b[k] for k \mmember{} [0,n])
Date html generated:
2020_05_20-AM-11_11_05
Last ObjectModification:
2020_01_06-PM-00_25_48
Theory : reals
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