Nuprl Lemma : primed-class-opt-single-val0
∀[Info,B:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(B)]. ∀[init:Id ⟶ bag(B)].
∀e:E. ∀v1,v2:B.
(single-valued-bag(init loc(e);B)
⇒ single-valued-classrel(es;X;B)
⇒ v1 ∈ Prior(X)?init(e)
⇒ v2 ∈ Prior(X)?init(e)
⇒ (v1 = v2 ∈ B))
Proof
Definitions occuring in Statement :
primed-class-opt: Prior(X)?b,
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,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
or: P ∨ Q,
exists: ∃x:A. B[x],
single-valued-bag: single-valued-bag(b;T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
es-p-local-pred: es-p-local-pred(es;P),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
es-locl: (e <loc e'),
not: ¬A,
false: False,
guard: {T},
single-valued-classrel: single-valued-classrel(es;X;T)
Latex:
\mforall{}[Info,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(B)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)].
\mforall{}e:E. \mforall{}v1,v2:B.
(single-valued-bag(init loc(e);B)
{}\mRightarrow{} single-valued-classrel(es;X;B)
{}\mRightarrow{} v1 \mmember{} Prior(X)?init(e)
{}\mRightarrow{} v2 \mmember{} Prior(X)?init(e)
{}\mRightarrow{} (v1 = v2))
Date html generated:
2016_05_17-AM-09_16_18
Last ObjectModification:
2016_01_17-PM-11_13_41
Theory : classrel!lemmas
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