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