Nuprl Lemma : firstn-before
∀[the_es:EO]. ∀[e:E]. ∀[n:ℕ]. firstn(n;before(e)) ~ before(before(e)[n]) supposing n < ||before(e)||
Proof
Definitions occuring in Statement :
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],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
nat: ℕ,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
and: P ∧ Q,
guard: {T},
subtype_rel: A ⊆r B,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
es-before: before(e),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
firstn: firstn(n;as),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
select: L[n],
nil: [],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
bfalse: ff,
sq_type: SQType(T),
cons: [a / b]
Latex:
\mforall{}[the$_{es}$:EO]. \mforall{}[e:E]. \mforall{}[n:\mBbbN{}]. firstn(n;before(e)) \msim{} before(before(e)[n]) su\000Cpposing n < ||before(e)||
Date html generated:
2016_05_16-AM-09_35_36
Last ObjectModification:
2016_01_17-PM-01_28_44
Theory : new!event-ordering
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