Nuprl Lemma : Memory-class-single-val2
∀[Info,A,S:Type]. ∀[init:Id ⟶ bag(S)]. ∀[f:A ⟶ S ⟶ S]. ∀[X:EClass(A)].
∀es:EO+(Info). ∀e:E. ∀s1,s2:S.
(single-valued-classrel(es;X;A)
⇒ single-valued-bag(init loc(e);S)
⇒ s1 ∈ Memory-class(f;init;X)(e)
⇒ s2 ∈ Memory-class(f;init;X)(e)
⇒ (s1 = s2 ∈ S))
Proof
Definitions occuring in Statement :
Memory-class: Memory-class(f;init;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,
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],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
or: P ∨ Q,
single-valued-bag: single-valued-bag(b;T),
not: ¬A,
false: False,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
es-E: E,
es-base-E: es-base-E(es),
true: True,
guard: {T},
rev_implies: P ⇐ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
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). \mforall{}e:E. \mforall{}s1,s2:S.
(single-valued-classrel(es;X;A)
{}\mRightarrow{} single-valued-bag(init loc(e);S)
{}\mRightarrow{} s1 \mmember{} Memory-class(f;init;X)(e)
{}\mRightarrow{} s2 \mmember{} Memory-class(f;init;X)(e)
{}\mRightarrow{} (s1 = s2))
Date html generated:
2016_05_17-AM-09_23_41
Last ObjectModification:
2016_01_17-PM-11_10_42
Theory : classrel!lemmas
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