Nuprl Definition : mrecind

mrecind(L;x.P[x]) ==
  ∀k:mKinds. ∀lbl:{lbl:Atom| 0 < ||mrec-spec(L;lbl;k)||} . ∀t:tuple-type(prec-arg-types(lbl,p.mrec-spec(L;lbl;p);k;lbl))\000C.
    ((∀j:ℕ||mrec-spec(L;lbl;k)||
        case mrec-spec(L;lbl;k)[j] of inl(y) => case of inl(p) => P[<p, t.j>inr(p) => (∀u∈t.j.P[<p, u>]) inr(_) \000C=> True)
     P[<k, mk-prec(lbl;t)>])



Definitions occuring in Statement :  mkinds: mKinds mrec-spec: mrec-spec(L;lbl;p) mk-prec: mk-prec(lbl;x) prec-arg-types: prec-arg-types(lbl,p.a[lbl; p];i;lbl) select-tuple: x.n tuple-type: tuple-type(L) l_all: (∀x∈L.P[x]) select: L[n] length: ||as|| int_seg: {i..j-} less_than: a < b all: x:A. B[x] implies:  Q true: True set: {x:A| B[x]}  pair: <a, b> decide: case of inl(x) => s[x] inr(y) => t[y] natural_number: $n atom: Atom
Definitions occuring in definition :  mkinds: mKinds set: {x:A| B[x]}  atom: Atom less_than: a < b tuple-type: tuple-type(L) prec-arg-types: prec-arg-types(lbl,p.a[lbl; p];i;lbl) implies:  Q all: x:A. B[x] int_seg: {i..j-} natural_number: $n select: L[n] decide: case of inl(x) => s[x] inr(y) => t[y] l_all: (∀x∈L.P[x]) select-tuple: x.n length: ||as|| mrec-spec: mrec-spec(L;lbl;p) true: True pair: <a, b> mk-prec: mk-prec(lbl;x)
FDL editor aliases :  mrecind

Latex:
mrecind(L;x.P[x])  ==
    \mforall{}k:mKinds.  \mforall{}lbl:\{lbl:Atom|  0  <  ||mrec-spec(L;lbl;k)||\}  .
    \mforall{}t:tuple-type(prec-arg-types(lbl,p.mrec-spec(L;lbl;p);k;lbl)).
        ((\mforall{}j:\mBbbN{}||mrec-spec(L;lbl;k)||
                case  mrec-spec(L;lbl;k)[j]
                  of  inl(y)  =>
                  case  y  of  inl(p)  =>  P[<p,  t.j>]  |  inr(p)  =>  (\mforall{}u\mmember{}t.j.P[<p,  u>])
                  |  inr($_{}$)  =>
                  True)
        {}\mRightarrow{}  P[<k,  mk-prec(lbl;t)>])



Date html generated: 2019_06_20-PM-02_15_54
Last ObjectModification: 2019_02_28-PM-04_51_59

Theory : tuples


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