Nuprl Lemma : State-class-single-val0
∀[Info,A,B:Type]. ∀[es:EO+(Info)]. ∀[f:A ⟶ B ⟶ B]. ∀[X:EClass(A)]. ∀[init:Id ⟶ bag(B)]. ∀[e:E]. ∀[v1,v2:B].
(v1 = v2 ∈ B) supposing
(v1 ∈ State-class(init;f;X)(e) and
v2 ∈ State-class(init;f;X)(e) and
single-valued-bag(init loc(e);B) and
single-valued-classrel(es;X;A))
Proof
Definitions occuring in Statement :
State-class: State-class(init;f;X),
single-valued-classrel: single-valued-classrel(es;X;T),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
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],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
prop: ℙ
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X:EClass(A)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[e:E].
\mforall{}[v1,v2:B].
(v1 = v2) supposing
(v1 \mmember{} State-class(init;f;X)(e) and
v2 \mmember{} State-class(init;f;X)(e) and
single-valued-bag(init loc(e);B) and
single-valued-classrel(es;X;A))
Date html generated:
2016_05_17-AM-09_35_55
Last ObjectModification:
2015_12_29-PM-03_57_46
Theory : classrel!lemmas
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