Nuprl Lemma : nearby-frs-mesh
∀e:{e:ℝ| r0 < e} . ∀p,q:ℝ List. (nearby-partitions(e;q;p) ⇒ (frs-mesh(p) ≤ (frs-mesh(q) + (r(2) * e))))
Proof
Definitions occuring in Statement :
nearby-partitions: nearby-partitions(e;p;q),
frs-mesh: frs-mesh(p),
rleq: x ≤ y,
rless: x < y,
rmul: a * b,
radd: a + b,
int-to-real: r(n),
real: ℝ,
list: T List,
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
frs-mesh: frs-mesh(p),
nearby-partitions: nearby-partitions(e;p;q),
and: P ∧ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
prop: ℙ,
ge: i ≥ j ,
sq_type: SQType(T),
guard: {T},
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
le: A ≤ B,
less_than': less_than'(a;b),
sq_stable: SqStable(P),
squash: ↓T,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
int_seg: {i..j-},
lelt: i ≤ j < k,
less_than: a < b,
rev_uimplies: rev_uimplies(P;Q),
rge: x ≥ y,
req_int_terms: t1 ≡ t2
Latex:
\mforall{}e:\{e:\mBbbR{}| r0 < e\} . \mforall{}p,q:\mBbbR{} List.
(nearby-partitions(e;q;p) {}\mRightarrow{} (frs-mesh(p) \mleq{} (frs-mesh(q) + (r(2) * e))))
Date html generated:
2020_05_20-AM-11_36_58
Last ObjectModification:
2020_01_06-PM-00_17_53
Theory : reals
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