Nuprl Lemma : list-max-aux_wf
∀[T:Type]. ∀[f:T ⟶ ℤ]. ∀[L:T List]. (list-max-aux(x.f[x];L) ∈ i:ℤ × {x:T| f[x] = i ∈ ℤ} + Top)
Proof
Definitions occuring in Statement :
list-max-aux: list-max-aux(x.f[x];L)
,
list: T List
,
uall: ∀[x:A]. B[x]
,
top: Top
,
so_apply: x[s]
,
member: t ∈ T
,
set: {x:A| B[x]}
,
function: x:A ⟶ B[x]
,
product: x:A × B[x]
,
union: left + right
,
int: ℤ
,
universe: Type
,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
list-max-aux: list-max-aux(x.f[x];L)
,
so_apply: x[s]
,
prop: ℙ
,
top: Top
,
so_lambda: λ2x y.t[x; y]
,
has-value: (a)↓
,
uimplies: b supposing a
,
pi1: fst(t)
,
all: ∀x:A. B[x]
,
implies: P
⇒ Q
,
bool: 𝔹
,
unit: Unit
,
it: ⋅
,
btrue: tt
,
ifthenelse: if b then t else f fi
,
uiff: uiff(P;Q)
,
and: P ∧ Q
,
subtype_rel: A ⊆r B
,
bfalse: ff
,
exists: ∃x:A. B[x]
,
or: P ∨ Q
,
sq_type: SQType(T)
,
guard: {T}
,
bnot: ¬bb
,
assert: ↑b
,
false: False
,
not: ¬A
,
so_apply: x[s1;s2]
Lemmas referenced :
list_accum_wf,
equal-wf-T-base,
top_wf,
value-type-has-value,
int-value-type,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
equal_wf,
int_subtype_base,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
less_than_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
unionEquality,
productEquality,
intEquality,
setEquality,
because_Cache,
hypothesis,
inrEquality,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaEquality,
callbyvalueReduce,
independent_isectElimination,
applyEquality,
functionExtensionality,
unionElimination,
productElimination,
lambdaFormation,
equalityElimination,
inlEquality,
dependent_pairEquality,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
independent_functionElimination,
setElimination,
rename,
axiomEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[f:T {}\mrightarrow{} \mBbbZ{}]. \mforall{}[L:T List]. (list-max-aux(x.f[x];L) \mmember{} i:\mBbbZ{} \mtimes{} \{x:T| f[x] = i\} + Top)
Date html generated:
2017_04_17-AM-07_40_25
Last ObjectModification:
2017_02_27-PM-04_13_57
Theory : list_1
Home
Index