Nuprl Lemma : find-maximal-consecutive_wf
∀[T:Type]. ∀[g:T ⟶ ℤ]. ∀[L:T List+]. (find-maximal-consecutive(g;L) ∈ {1..||L|| + 1-})
Proof
Definitions occuring in Statement :
find-maximal-consecutive: find-maximal-consecutive(g;L),
listp: A List+,
length: ||as||,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
listp: A List+,
find-maximal-consecutive: find-maximal-consecutive(g;L),
all: ∀x:A. B[x],
or: P ∨ Q,
ge: i ≥ j ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
true: True,
not: ¬A,
implies: P ⇒ Q,
false: False,
cons: [a / b],
top: Top,
uimplies: b supposing a,
nat: ℕ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
pi1: fst(t),
colength: colength(L),
guard: {T},
decidable: Dec(P),
nil: [],
it: ⋅,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
int_seg: {i..j-},
lelt: i ≤ j < k,
has-value: (a)↓,
bool: 𝔹,
unit: Unit,
btrue: tt,
uiff: uiff(P;Q),
bfalse: ff,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
nequal: a ≠ b ∈ T
Latex:
\mforall{}[T:Type]. \mforall{}[g:T {}\mrightarrow{} \mBbbZ{}]. \mforall{}[L:T List\msupplus{}]. (find-maximal-consecutive(g;L) \mmember{} \{1..||L|| + 1\msupminus{}\})
Date html generated:
2016_05_17-PM-00_56_47
Last ObjectModification:
2016_01_18-AM-07_41_43
Theory : event-logic-applications
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