Nuprl Lemma : C_LVALUE-proper-Indexed
∀env:C_TYPE_env(). ∀lval:C_LVALUE(). ∀i:ℤ.
((↑C_LVALUE-proper(env;LV_Index(lval;i))) ⇒ (↑C_Array?(outl(C_TYPE-of-LVALUE(env;lval)))))
Proof
Definitions occuring in Statement :
C_LVALUE-proper: C_LVALUE-proper(env;lval),
C_TYPE-of-LVALUE: C_TYPE-of-LVALUE(env;lval),
C_TYPE_env: C_TYPE_env(),
LV_Index: LV_Index(lval;idx),
C_LVALUE: C_LVALUE(),
C_Array?: C_Array?(v),
outl: outl(x),
assert: ↑b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
assert: ↑b,
ifthenelse: if b then t else f fi ,
LV_Index?: LV_Index?(v),
eq_atom: x =a y,
pi1: fst(t),
LV_Index: LV_Index(lval;idx),
btrue: tt,
true: True,
let: let,
LV_Index-lval: LV_Index-lval(v),
pi2: snd(t),
LV_Index-idx: LV_Index-idx(v),
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
C_LVALUE-proper-Index,
LV_Index_wf,
assert_wf,
C_LVALUE-proper_wf,
C_LVALUE_wf,
C_TYPE_env_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
hypothesis,
independent_functionElimination,
natural_numberEquality,
sqequalRule,
productElimination,
intEquality
Latex:
\mforall{}env:C\_TYPE\_env(). \mforall{}lval:C\_LVALUE(). \mforall{}i:\mBbbZ{}.
((\muparrow{}C\_LVALUE-proper(env;LV\_Index(lval;i))) {}\mRightarrow{} (\muparrow{}C\_Array?(outl(C\_TYPE-of-LVALUE(env;lval)))))
Date html generated:
2016_05_16-AM-08_48_30
Last ObjectModification:
2015_12_28-PM-06_56_16
Theory : C-semantics
Home
Index