Nuprl Lemma : infn_wf
∀[I:{I:Interval| icompact(I)} ]
∀n:ℕ
(infn(n;I) ∈ {F:{f:I^n ⟶ ℝ| ∀a,b:I^n. (req-vec(n;a;b) ⇒ ((f a) = (f b)))} ⟶ ℝ|
∀f,g:{f:I^n ⟶ ℝ| ∀a,b:I^n. (req-vec(n;a;b) ⇒ ((f a) = (f b)))} .
((∀x:I^n. ((f x) = (g x))) ⇒ ((F f) = (F g)))} )
Proof
Definitions occuring in Statement :
infn: infn(n;I),
interval-vec: I^n,
req-vec: req-vec(n;x;y),
icompact: icompact(I),
interval: Interval,
req: x = y,
real: ℝ,
nat: ℕ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
infn: infn(n;I),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
and: P ∧ Q,
prop: ℙ,
less_than': less_than'(a;b),
le: A ≤ B,
lelt: i ≤ j < k,
int_seg: {i..j-},
real-vec: ℝ^n,
interval-vec: I^n,
subtype_rel: A ⊆r B,
top: Top,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
bfalse: ff,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
decidable: Dec(P),
subtract: n - m,
sq_stable: SqStable(P),
squash: ↓T,
nat_plus: ℕ+,
cand: A c∧ B,
rev_uimplies: rev_uimplies(P;Q),
so_lambda: λ2x.t[x],
so_apply: x[s],
real-vec-extend: a++z,
req-vec: req-vec(n;x;y)
Latex:
\mforall{}[I:\{I:Interval| icompact(I)\} ]
\mforall{}n:\mBbbN{}
(infn(n;I) \mmember{} \{F:\{f:I\^{}n {}\mrightarrow{} \mBbbR{}| \mforall{}a,b:I\^{}n. (req-vec(n;a;b) {}\mRightarrow{} ((f a) = (f b)))\} {}\mrightarrow{} \mBbbR{}|
\mforall{}f,g:\{f:I\^{}n {}\mrightarrow{} \mBbbR{}| \mforall{}a,b:I\^{}n. (req-vec(n;a;b) {}\mRightarrow{} ((f a) = (f b)))\} .
((\mforall{}x:I\^{}n. ((f x) = (g x))) {}\mRightarrow{} ((F f) = (F g)))\} )
Date html generated:
2020_05_20-PM-00_38_31
Last ObjectModification:
2020_01_07-AM-10_26_58
Theory : reals
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