Nuprl Lemma : rprod_functionality
∀[n,m:ℤ]. ∀[x,y:{n..m + 1-} ⟶ ℝ]. rprod(n;m;k.x[k]) = rprod(n;m;k.y[k]) supposing x[k] = y[k] for k ∈ [n,m]
Proof
Definitions occuring in Statement :
rprod: rprod(n;m;k.x[k]),
pointwise-req: x[k] = y[k] for k ∈ [n,m],
req: x = y,
real: ℝ,
int_seg: {i..j-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
nat: ℕ,
false: False,
ge: i ≥ j ,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
and: P ∧ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
less_than: a < b,
squash: ↓T,
decidable: Dec(P),
or: P ∨ Q,
rprod: rprod(n;m;k.x[k]),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
pointwise-req: x[k] = y[k] for k ∈ [n,m],
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[n,m:\mBbbZ{}]. \mforall{}[x,y:\{n..m + 1\msupminus{}\} {}\mrightarrow{} \mBbbR{}].
rprod(n;m;k.x[k]) = rprod(n;m;k.y[k]) supposing x[k] = y[k] for k \mmember{} [n,m]
Date html generated:
2020_05_20-AM-11_12_34
Last ObjectModification:
2020_03_20-AM-10_40_13
Theory : reals
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