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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
C_LVALUE_ind: C_LVALUE_ind,
so_apply: x[s1;s2;s3],
so_apply: x[s],
so_apply: x[s1;s2],
C_LVALUE-definition,
C_LVALUE-induction,
uniform-comp-nat-induction,
C_LVALUE-ext,
eq_atom: x =a y,
bool_cases_sqequal,
eqff_to_assert,
any: any x,
btrue: tt,
bfalse: ff,
it: ⋅,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
prop: ℙ,
guard: {T},
or: P ∨ Q,
squash: ↓T,
subtype_rel: A ⊆r B
Lemmas referenced :
C_LVALUE-definition,
C_LVALUE-induction,
uniform-comp-nat-induction,
C_LVALUE-ext,
bool_cases_sqequal,
eqff_to_assert,
set_wf,
all_wf,
LV_Scomp_wf,
LV_Index_wf,
LV_Ground_wf,
C_LOCATION_wf,
C_LVALUE_wf,
base_wf,
lifting-strict-atom_eq,
is-exception_wf,
has-value_wf_base,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
thin,
lemma_by_obid,
hypothesis,
lambdaFormation,
because_Cache,
sqequalSqle,
divergentSqle,
callbyvalueDecide,
sqequalHypSubstitution,
unionEquality,
unionElimination,
sqleReflexivity,
equalityEquality,
equalityTransitivity,
equalitySymmetry,
hypothesisEquality,
dependent_functionElimination,
independent_functionElimination,
decideExceptionCases,
axiomSqleEquality,
exceptionSqequal,
baseApply,
closedConclusion,
baseClosed,
isectElimination,
independent_isectElimination,
independent_pairFormation,
inrFormation,
imageMemberEquality,
imageElimination,
inlFormation,
instantiate,
extract_by_obid,
applyEquality,
lambdaEquality,
isectEquality,
functionEquality,
cumulativity,
universeEquality,
setEquality,
intEquality,
setElimination,
rename,
atomEquality,
dependent_set_memberEquality,
axiomEquality
Latex:
\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:
2016_05_16-AM-08_47_45
Last ObjectModification:
2016_01_17-AM-09_43_58
Theory : C-semantics
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