Nuprl Lemma : split-maximal-consecutive_wf
∀[T:Type]. ∀[g:T ⟶ ℤ]. ∀[L:T List+].
(split-maximal-consecutive(g;L) ∈ {p:T List+ × (T List)| L = ((fst(p)) @ (snd(p))) ∈ (T List)} )
Proof
Definitions occuring in Statement :
split-maximal-consecutive: split-maximal-consecutive(g;L),
listp: A List+,
append: as @ bs,
list: T List,
uall: ∀[x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
product: x:A × B[x],
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
split-maximal-consecutive: split-maximal-consecutive(g;L),
listp: A List+,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
uimplies: b supposing a,
int_seg: {i..j-},
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
top: Top,
squash: ↓T,
prop: ℙ,
int_iseg: {i...j},
lelt: i ≤ j < k,
and: P ∧ Q,
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
less_than: a < b,
uiff: uiff(P;Q),
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
pi1: fst(t),
pi2: snd(t)
Latex:
\mforall{}[T:Type]. \mforall{}[g:T {}\mrightarrow{} \mBbbZ{}]. \mforall{}[L:T List\msupplus{}].
(split-maximal-consecutive(g;L) \mmember{} \{p:T List\msupplus{} \mtimes{} (T List)| L = ((fst(p)) @ (snd(p)))\} )
Date html generated:
2016_05_17-PM-00_57_00
Last ObjectModification:
2016_01_18-AM-07_39_26
Theory : event-logic-applications
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