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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