Nuprl Lemma : C_LVALUE-definition
∀[A:Type]. ∀[R:A ⟶ C_LVALUE() ⟶ ℙ].
((∀loc:C_LOCATION(). {x:A| R[x;LV_Ground(loc)]} )
⇒ (∀lval:C_LVALUE(). ∀idx:ℤ. ({x:A| R[x;lval]} ⇒ {x:A| R[x;LV_Index(lval;idx)]} ))
⇒ (∀lval:C_LVALUE(). ∀comp:Atom. ({x:A| R[x;lval]} ⇒ {x:A| R[x;LV_Scomp(lval;comp)]} ))
⇒ {∀v:C_LVALUE(). {x:A| R[x;v]} })
Proof
Definitions occuring in Statement :
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,
guard: {T},
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
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],
implies: P ⇒ Q,
guard: {T},
so_lambda: λ2x.t[x],
member: t ∈ T,
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
so_apply: x[s],
prop: ℙ
Lemmas referenced :
C_LVALUE-induction,
set_wf,
C_LVALUE_wf,
all_wf,
LV_Scomp_wf,
LV_Index_wf,
C_LOCATION_wf,
LV_Ground_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
hypothesisEquality,
applyEquality,
because_Cache,
independent_functionElimination,
atomEquality,
functionEquality,
universeEquality,
intEquality,
cumulativity
Latex:
\mforall{}[A:Type]. \mforall{}[R:A {}\mrightarrow{} C\_LVALUE() {}\mrightarrow{} \mBbbP{}].
((\mforall{}loc:C\_LOCATION(). \{x:A| R[x;LV\_Ground(loc)]\} )
{}\mRightarrow{} (\mforall{}lval:C\_LVALUE(). \mforall{}idx:\mBbbZ{}. (\{x:A| R[x;lval]\} {}\mRightarrow{} \{x:A| R[x;LV\_Index(lval;idx)]\} ))
{}\mRightarrow{} (\mforall{}lval:C\_LVALUE(). \mforall{}comp:Atom. (\{x:A| R[x;lval]\} {}\mRightarrow{} \{x:A| R[x;LV\_Scomp(lval;comp)]\} ))
{}\mRightarrow{} \{\mforall{}v:C\_LVALUE(). \{x:A| R[x;v]\} \})
Date html generated:
2016_05_16-AM-08_47_40
Last ObjectModification:
2015_12_28-PM-06_56_51
Theory : C-semantics
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