Nuprl Lemma : loop-class-memory-single-val
∀[Info,B:Type]. ∀[init:Id ⟶ bag(B)]. ∀[X:EClass(B ⟶ B)]. ∀[es:EO+(Info)].
(single-valued-classrel(es;loop-class-memory(X;init);B)) supposing
((∀l:Id. single-valued-bag(init l;B)) and
single-valued-classrel(es;X;B ⟶ B))
Proof
Definitions occuring in Statement :
loop-class-memory: loop-class-memory(X;init),
single-valued-classrel: single-valued-classrel(es;X;T),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
single-valued-bag: single-valued-bag(b;T),
bag: bag(T)
Definitions unfolded in proof :
single-valued-classrel: single-valued-classrel(es;X;T),
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
uall: ∀[x:A]. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
uiff: uiff(P;Q),
sq_type: SQType(T),
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
single-valued-bag: single-valued-bag(b;T)
Latex:
\mforall{}[Info,B:Type]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[X:EClass(B {}\mrightarrow{} B)]. \mforall{}[es:EO+(Info)].
(single-valued-classrel(es;loop-class-memory(X;init);B)) supposing
((\mforall{}l:Id. single-valued-bag(init l;B)) and
single-valued-classrel(es;X;B {}\mrightarrow{} B))
Date html generated:
2016_05_16-PM-11_40_59
Last ObjectModification:
2016_01_17-PM-07_03_49
Theory : event-ordering
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