Nuprl Lemma : iterated_classrel-single-val
∀[Info,A,S:Type]. ∀[init:Id ⟶ bag(S)]. ∀[f:A ⟶ S ⟶ S]. ∀[X:EClass(A)].
∀es:EO+(Info)
(single-valued-classrel(es;X;A)
⇒ (∀e:E
(single-valued-bag(init loc(e);S)
⇒ (∀v1,v2:S.
(iterated_classrel(es;S;A;f;init;X;e;v1)
⇒ iterated_classrel(es;S;A;f;init;X;e;v2)
⇒ (v1 = v2 ∈ S))))))
Proof
Definitions occuring in Statement :
iterated_classrel: iterated_classrel(es;S;A;f;init;X;e;v),
single-valued-classrel: single-valued-classrel(es;X;T),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
single-valued-bag: single-valued-bag(b;T),
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
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,
iterated_classrel: iterated_classrel(es;S;A;f;init;X;e;v),
sq_type: SQType(T),
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
single-valued-bag: single-valued-bag(b;T),
single-valued-classrel: single-valued-classrel(es;X;T),
es-E: E,
es-base-E: es-base-E(es),
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[Info,A,S:Type]. \mforall{}[init:Id {}\mrightarrow{} bag(S)]. \mforall{}[f:A {}\mrightarrow{} S {}\mrightarrow{} S]. \mforall{}[X:EClass(A)].
\mforall{}es:EO+(Info)
(single-valued-classrel(es;X;A)
{}\mRightarrow{} (\mforall{}e:E
(single-valued-bag(init loc(e);S)
{}\mRightarrow{} (\mforall{}v1,v2:S.
(iterated\_classrel(es;S;A;f;init;X;e;v1)
{}\mRightarrow{} iterated\_classrel(es;S;A;f;init;X;e;v2)
{}\mRightarrow{} (v1 = v2))))))
Date html generated:
2016_05_16-PM-01_47_55
Last ObjectModification:
2016_01_17-PM-07_46_01
Theory : event-ordering
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