Nuprl Lemma : accum-class-val
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[base,f:Top]. ∀[e:E].
accum-class(a,x.f[a;x];x.base[x];X)(e) ~ accum_list(a,e.f[a;X(e)];e.base[X(e)];≤(X)(e))
supposing ↑e ∈b accum-class(a,x.f[a;x];x.base[x];X)
Proof
Definitions occuring in Statement :
accum-class: accum-class(a,x.f[a; x];x.base[x];X),
es-interface-predecessors: ≤(X)(e),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
accum_list: accum_list(a,x.f[a; x];x.base[x];L),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
so_apply: x[s],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
accum-class: accum-class(a,x.f[a; x];x.base[x];X),
in-eclass: e ∈b X,
eclass-val: X(e),
member: t ∈ T,
uall: ∀[x:A]. B[x],
eclass: EClass(A[eo; e]),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
nat: ℕ,
ifthenelse: if b then t else f fi ,
top: Top,
eq_int: (i =z j),
assert: ↑b,
prop: ℙ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
false: False,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[base,f:Top]. \mforall{}[e:E].
accum-class(a,x.f[a;x];x.base[x];X)(e) \msim{} accum\_list(a,e.f[a;X(e)];e.base[X(e)];\mleq{}(X)(e))
supposing \muparrow{}e \mmember{}\msubb{} accum-class(a,x.f[a;x];x.base[x];X)
Date html generated:
2016_05_16-PM-11_09_42
Last ObjectModification:
2015_12_29-AM-10_34_48
Theory : event-ordering
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