Nuprl Lemma : find-combine_wf
∀[T:Type]. ∀[cmp:T ⟶ ℤ]. ∀[l:T List]. (find-combine(cmp;l) ∈ T?)
Proof
Definitions occuring in Statement :
find-combine: find-combine(cmp;l),
list: T List,
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
find-combine: find-combine(cmp;l),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
has-value: (a)↓,
uimplies: b supposing a,
so_apply: x[s1;s2;s3]
Lemmas referenced :
list_ind_wf,
unit_wf2,
it_wf,
value-type-has-value,
int-value-type,
ifthenelse_wf,
eq_int_wf,
lt_int_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
unionEquality,
because_Cache,
hypothesis,
inrEquality,
lambdaEquality,
callbyvalueReduce,
intEquality,
independent_isectElimination,
applyEquality,
natural_numberEquality,
inlEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[cmp:T {}\mrightarrow{} \mBbbZ{}]. \mforall{}[l:T List]. (find-combine(cmp;l) \mmember{} T?)
Date html generated:
2016_05_14-PM-02_40_10
Last ObjectModification:
2015_12_26-PM-02_44_42
Theory : list_1
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