Nuprl Lemma : es-open-interval-ordered-iff
∀es:EO. ∀e1,e2:E. ∀n1,n2:ℕ||(e1, e2)||. (n1 < n2 ⇐⇒ ((e1, e2)[n1] <loc (e1, e2)[n2]))
Proof
Definitions occuring in Statement :
es-open-interval: (e, e'),
es-locl: (e <loc e'),
es-E: E,
event_ordering: EO,
select: L[n],
length: ||as||,
int_seg: {i..j-},
less_than: a < b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
int_seg: {i..j-},
rev_implies: P ⇐ Q,
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
sq_type: SQType(T),
less_than: a < b,
squash: ↓T
Latex:
\mforall{}es:EO. \mforall{}e1,e2:E. \mforall{}n1,n2:\mBbbN{}||(e1, e2)||. (n1 < n2 \mLeftarrow{}{}\mRightarrow{} ((e1, e2)[n1] <loc (e1, e2)[n2]))
Date html generated:
2016_05_16-AM-09_36_22
Last ObjectModification:
2016_01_17-PM-01_28_06
Theory : new!event-ordering
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