Nuprl Lemma : firstn-le-before
∀[the_es:EO]. ∀[e:E]. ∀[n:ℕ]. firstn(n + 1;≤loc(e)) ~ ≤loc(before(e)[n]) supposing n < ||before(e)||
Proof
Definitions occuring in Statement :
es-le-before: ≤loc(e),
es-before: before(e),
es-E: E,
event_ordering: EO,
firstn: firstn(n;as),
select: L[n],
length: ||as||,
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nat: ℕ,
prop: ℙ,
es-le-before: ≤loc(e),
subtype_rel: A ⊆r B,
top: Top,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
less_than: a < b,
squash: ↓T
Latex:
\mforall{}[the$_{es}$:EO]. \mforall{}[e:E]. \mforall{}[n:\mBbbN{}]. firstn(n + 1;\mleq{}loc(e)) \msim{} \mleq{}loc(before(e)[n]) su\000Cpposing n < ||before(e)||
Date html generated:
2016_05_16-AM-09_35_55
Last ObjectModification:
2016_01_17-PM-01_27_57
Theory : new!event-ordering
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