Nuprl Lemma : C_STOREp-welltyped_wf
∀env:C_TYPE_env(). ∀store:C_STOREp().  (C_STOREp-welltyped(env;store) ∈ ℙ)
Proof
Definitions occuring in Statement : 
C_STOREp-welltyped: C_STOREp-welltyped(env;store)
, 
C_STOREp: C_STOREp()
, 
C_TYPE_env: C_TYPE_env()
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
C_STOREp-welltyped: C_STOREp-welltyped(env;store)
, 
uall: ∀[x:A]. B[x]
, 
so_lambda: λ2x.t[x]
, 
C_TYPE_env: C_TYPE_env()
, 
implies: P 
⇒ Q
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
ifthenelse: if b then t else f fi 
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
C_STOREp: C_STOREp()
, 
band: p ∧b q
, 
outl: outl(x)
, 
isl: isl(x)
, 
prop: ℙ
, 
not: ¬A
, 
false: False
, 
bfalse: ff
, 
exists: ∃x:A. B[x]
, 
or: P ∨ Q
, 
sq_type: SQType(T)
, 
guard: {T}
, 
bnot: ¬bb
, 
assert: ↑b
, 
so_apply: x[s]
Lemmas referenced : 
all_wf, 
C_LOCATION_wf, 
isl_wf, 
C_TYPE_wf, 
unit_wf2, 
bool_wf, 
eqtt_to_assert, 
assert_wf, 
C_DVALUEp_wf, 
C_TYPE_vs_DVALp_wf, 
assert_elim, 
bfalse_wf, 
and_wf, 
equal_wf, 
btrue_neq_bfalse, 
eqff_to_assert, 
bool_cases_sqequal, 
subtype_base_sq, 
bool_subtype_base, 
assert-bnot, 
isr_wf, 
C_STOREp_wf, 
C_TYPE_env_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
cut, 
sqequalRule, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesis, 
lambdaEquality, 
applyEquality, 
hypothesisEquality, 
unionElimination, 
equalityElimination, 
productElimination, 
independent_isectElimination, 
because_Cache, 
dependent_functionElimination, 
unionEquality, 
equalityTransitivity, 
equalitySymmetry, 
dependent_set_memberEquality, 
independent_pairFormation, 
setElimination, 
rename, 
setEquality, 
independent_functionElimination, 
voidElimination, 
equalityEquality, 
dependent_pairFormation, 
promote_hyp, 
instantiate, 
cumulativity
Latex:
\mforall{}env:C\_TYPE\_env().  \mforall{}store:C\_STOREp().    (C\_STOREp-welltyped(env;store)  \mmember{}  \mBbbP{})
Date html generated:
2016_05_16-AM-08_51_29
Last ObjectModification:
2015_12_28-PM-06_54_55
Theory : C-semantics
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