Nuprl Lemma : C_LVALUE-proper-Ground
∀env:C_TYPE_env(). ∀lval:C_LVALUE().
((↑LV_Ground?(lval)) ⇒ (↑C_LVALUE-proper(env;lval)) ⇒ (↑isl(env LV_Ground-loc(lval))))
Proof
Definitions occuring in Statement :
C_LVALUE-proper: C_LVALUE-proper(env;lval),
C_TYPE_env: C_TYPE_env(),
LV_Ground-loc: LV_Ground-loc(v),
LV_Ground?: LV_Ground?(v),
C_LVALUE: C_LVALUE(),
assert: ↑b,
isl: isl(x),
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ,
C_TYPE_env: C_TYPE_env(),
uimplies: b supposing a,
so_apply: x[s],
LV_Ground: LV_Ground(loc),
LV_Ground-loc: LV_Ground-loc(v),
pi2: snd(t),
isl: isl(x),
C_LVALUE-proper: C_LVALUE-proper(env;lval),
C_TYPE-of-LVALUE: C_TYPE-of-LVALUE(env;lval),
C_LVALUE_ind: C_LVALUE_ind,
LV_Index: LV_Index(lval;idx),
LV_Ground?: LV_Ground?(v),
pi1: fst(t),
eq_atom: x =a y,
not: ¬A,
false: False,
LV_Scomp: LV_Scomp(lval;comp),
guard: {T}
Lemmas referenced :
C_LVALUE-induction,
assert_wf,
LV_Ground?_wf,
C_LVALUE-proper_wf,
isl_wf,
C_TYPE_wf,
unit_wf2,
LV_Ground-loc_wf,
C_LVALUE_wf,
LV_Ground_wf,
C_LOCATION_wf,
assert_elim,
LV_Index_wf,
bfalse_wf,
btrue_neq_bfalse,
LV_Scomp_wf,
C_TYPE_env_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
functionEquality,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
applyEquality,
independent_isectElimination,
independent_functionElimination,
addLevel,
levelHypothesis,
equalityTransitivity,
equalitySymmetry,
voidElimination,
intEquality,
atomEquality,
because_Cache
Latex:
\mforall{}env:C\_TYPE\_env(). \mforall{}lval:C\_LVALUE().
((\muparrow{}LV\_Ground?(lval)) {}\mRightarrow{} (\muparrow{}C\_LVALUE-proper(env;lval)) {}\mRightarrow{} (\muparrow{}isl(env LV\_Ground-loc(lval))))
Date html generated:
2016_05_16-AM-08_48_19
Last ObjectModification:
2015_12_28-PM-06_56_19
Theory : C-semantics
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