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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