Nuprl Lemma : es-subinterval
∀es:EO. ∀e2,e1:E. (e1 ≤loc e2 ⇒ (∀n:ℕ. (∃e∈(e1,e2].||[e1, pred(e)]|| = n ∈ ℤ) supposing (n < ||[e1, e2]|| and 0 < n))\000C)
Proof
Definitions occuring in Statement :
existse-between3: ∃e∈(e1,e2].P[e],
es-interval: [e, e'],
es-le: e ≤loc e' ,
es-pred: pred(e),
es-E: E,
event_ordering: EO,
length: ||as||,
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
uimplies: b supposing a,
nat: ℕ,
all: ∀x:A. B[x],
and: P ∧ Q,
so_apply: x[s],
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
guard: {T},
iff: P ⇐⇒ Q,
or: P ∨ Q,
cand: A c∧ B,
decidable: Dec(P),
existse-between3: ∃e∈(e1,e2].P[e],
exists: ∃x:A. B[x],
not: ¬A,
false: False,
true: True,
top: Top,
squash: ↓T,
subtype_rel: A ⊆r B,
ge: i ≥ j ,
less_than: a < b,
uiff: uiff(P;Q),
satisfiable_int_formula: satisfiable_int_formula(fmla)
Latex:
\mforall{}es:EO. \mforall{}e2,e1:E.
(e1 \mleq{}loc e2 {}\mRightarrow{} (\mforall{}n:\mBbbN{}. (\mexists{}e\mmember{}(e1,e2].||[e1, pred(e)]|| = n) supposing (n < ||[e1, e2]|| and 0 < n)))
Date html generated:
2016_05_16-AM-09_46_38
Last ObjectModification:
2016_01_17-PM-01_26_51
Theory : new!event-ordering
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