Nuprl Lemma : C_field_of_wf
∀[a:Atom]. ∀[ctyp:{t:C_TYPE()| ↑C_Struct?(t)} ].  (C_field_of(a;ctyp) ∈ 𝔹)
Proof
Definitions occuring in Statement : 
C_field_of: C_field_of(a;ctyp)
, 
C_Struct?: C_Struct?(v)
, 
C_TYPE: C_TYPE()
, 
assert: ↑b
, 
bool: 𝔹
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
set: {x:A| B[x]} 
, 
atom: Atom
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
C_field_of: C_field_of(a;ctyp)
, 
subtype_rel: A ⊆r B
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
uimplies: b supposing a
, 
all: ∀x:A. B[x]
, 
top: Top
, 
prop: ℙ
Lemmas referenced : 
deq-member_wf, 
atom-deq_wf, 
map_wf, 
C_TYPE_wf, 
pi1_wf_top, 
subtype_rel_product, 
top_wf, 
C_Struct-fields_wf, 
set_wf, 
assert_wf, 
C_Struct?_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
setElimination, 
thin, 
rename, 
sqequalRule, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
atomEquality, 
hypothesis, 
productEquality, 
lambdaEquality, 
hypothesisEquality, 
applyEquality, 
because_Cache, 
independent_isectElimination, 
lambdaFormation, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry
Latex:
\mforall{}[a:Atom].  \mforall{}[ctyp:\{t:C\_TYPE()|  \muparrow{}C\_Struct?(t)\}  ].    (C\_field\_of(a;ctyp)  \mmember{}  \mBbbB{})
Date html generated:
2016_05_16-AM-08_47_53
Last ObjectModification:
2015_12_28-PM-06_56_25
Theory : C-semantics
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