Nuprl Lemma : imax-list-as-reduce
∀[L:ℤ List]
  imax-list(L) = outl(reduce(λx,y. case y of inl(z) => inl imax(x;z) | inr(z) => inl x;inr ⋅ L)) ∈ ℤ supposing 0 < ||L|\000C|
Proof
Definitions occuring in Statement : 
imax-list: imax-list(L)
, 
length: ||as||
, 
reduce: reduce(f;k;as)
, 
list: T List
, 
imax: imax(a;b)
, 
outl: outl(x)
, 
less_than: a < b
, 
it: ⋅
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
lambda: λx.A[x]
, 
decide: case b of inl(x) => s[x] | inr(y) => t[y]
, 
inr: inr x 
, 
inl: inl x
, 
natural_number: $n
, 
int: ℤ
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
so_apply: x[s1;s2]
, 
assoc: Assoc(T;op)
, 
infix_ap: x f y
, 
squash: ↓T
, 
prop: ℙ
, 
true: True
, 
subtype_rel: A ⊆r B
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
rev_implies: P 
⇐ Q
, 
implies: P 
⇒ Q
, 
comm: Comm(T;op)
, 
sq_type: SQType(T)
, 
all: ∀x:A. B[x]
, 
imax-list: imax-list(L)
Lemmas referenced : 
combine-list-as-reduce, 
imax_wf, 
equal_wf, 
squash_wf, 
true_wf, 
imax_assoc, 
iff_weakening_equal, 
imax_com, 
subtype_base_sq, 
int_subtype_base, 
imax-list_wf, 
less_than_wf, 
length_wf, 
list_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
intEquality, 
lambdaEquality, 
hypothesisEquality, 
hypothesis, 
independent_isectElimination, 
sqequalRule, 
applyEquality, 
imageElimination, 
equalityTransitivity, 
equalitySymmetry, 
universeEquality, 
natural_numberEquality, 
imageMemberEquality, 
baseClosed, 
productElimination, 
independent_functionElimination, 
because_Cache, 
isect_memberEquality, 
axiomEquality, 
instantiate, 
cumulativity, 
dependent_functionElimination
Latex:
\mforall{}[L:\mBbbZ{}  List]
    imax-list(L)  =  outl(reduce(\mlambda{}x,y.  case  y  of  inl(z)  =>  inl  imax(x;z)  |  inr(z)  =>  inl  x;inr  \mcdot{}  ;L)) 
    supposing  0  <  ||L||
Date html generated:
2017_04_17-AM-07_39_59
Last ObjectModification:
2017_02_27-PM-04_12_41
Theory : list_1
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