Nuprl Lemma : C_LVALUE_ind_wf
∀[A:Type]. ∀[R:A ─→ C_LVALUE() ─→ ℙ]. ∀[v:C_LVALUE()]. ∀[Ground:loc:C_LOCATION() ─→ {x:A| R[x;LV_Ground(loc)]} ].
∀[Index:lval:C_LVALUE() ─→ idx:ℤ ─→ {x:A| R[x;lval]} ─→ {x:A| R[x;LV_Index(lval;idx)]} ].
∀[Scomp:lval:C_LVALUE() ─→ comp:Atom ─→ {x:A| R[x;lval]} ─→ {x:A| R[x;LV_Scomp(lval;comp)]} ].
(C_LVALUE_ind(v;
LV_Ground(loc)⇒ Ground[loc];
LV_Index(lval,idx)⇒ rec1.Index[lval;idx;rec1];
LV_Scomp(lval,comp)⇒ rec2.Scomp[lval;comp;rec2]) ∈ {x:A| R[x;v]} )
Proof
Definitions occuring in Statement :
C_LVALUE_ind: C_LVALUE_ind,
LV_Scomp: LV_Scomp(lval;comp),
LV_Index: LV_Index(lval;idx),
LV_Ground: LV_Ground(loc),
C_LVALUE: C_LVALUE(),
C_LOCATION: C_LOCATION(),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2;s3],
so_apply: x[s1;s2],
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
int: ℤ,
atom: Atom,
universe: Type
Lemmas :
top_wf,
has-value_wf_base,
lifting-strict-atom_eq,
base_wf,
C_LOCATION_wf,
LV_Ground_wf,
C_LVALUE_wf,
LV_Index_wf,
LV_Scomp_wf,
all_wf,
set_wf,
subtype_rel-equal
\mforall{}[A:Type]. \mforall{}[R:A {}\mrightarrow{} C\_LVALUE() {}\mrightarrow{} \mBbbP{}]. \mforall{}[v:C\_LVALUE()].
\mforall{}[Ground:loc:C\_LOCATION() {}\mrightarrow{} \{x:A| R[x;LV\_Ground(loc)]\} ]. \mforall{}[Index:lval:C\_LVALUE()
{}\mrightarrow{} idx:\mBbbZ{}
{}\mrightarrow{} \{x:A| R[x;lval]\}
{}\mrightarrow{} \{x:A|
R[x;LV\_Index(lval;idx)]\} ].
\mforall{}[Scomp:lval:C\_LVALUE() {}\mrightarrow{} comp:Atom {}\mrightarrow{} \{x:A| R[x;lval]\} {}\mrightarrow{} \{x:A| R[x;LV\_Scomp(lval;comp)]\} ].
(C\_LVALUE\_ind(v;
LV\_Ground(loc){}\mRightarrow{} Ground[loc];
LV\_Index(lval,idx){}\mRightarrow{} rec1.Index[lval;idx;rec1];
LV\_Scomp(lval,comp){}\mRightarrow{} rec2.Scomp[lval;comp;rec2]) \mmember{} \{x:A| R[x;v]\} )
Date html generated:
2015_07_17-AM-07_43_33
Last ObjectModification:
2015_01_29-PM-04_39_23
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