Nuprl Lemma : pred-member-es-open-interval
∀[es:EO]. ∀[e1,e2:E]. ∀[n:{1..||(e1, e2)||-}]. (pred((e1, e2)[n]) = (e1, e2)[n - 1] ∈ E)
Proof
Definitions occuring in Statement :
es-open-interval: (e, e'),
es-pred: pred(e),
es-E: E,
event_ordering: EO,
select: L[n],
length: ||as||,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
subtract: n - m,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_seg: {i..j-},
all: ∀x:A. B[x],
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
less_than: a < b,
squash: ↓T,
le: A ≤ B,
sq_type: SQType(T),
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
es-locl: (e <loc e'),
l_member: (x ∈ l),
nat: ℕ,
cand: A c∧ B,
ge: i ≥ j
Latex:
\mforall{}[es:EO]. \mforall{}[e1,e2:E]. \mforall{}[n:\{1..||(e1, e2)||\msupminus{}\}]. (pred((e1, e2)[n]) = (e1, e2)[n - 1])
Date html generated:
2016_05_16-AM-09_36_38
Last ObjectModification:
2016_01_17-PM-01_32_00
Theory : new!event-ordering
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