Nuprl Lemma : eclass2-single-val
∀[Info,B,C:Type]. ∀[X:EClass(B ⟶ bag(C))]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)].
(single-valued-classrel(es;(X o Y);C)) supposing
(single-valued-classrel(es;X;B ⟶ bag(C)) and
single-valued-classrel(es;Y;B) and
(∀b:B. ∀cs:bag(C). ∀es:EO+(Info). ∀e:E. (cs ∈ X(b)(e) ⇒ single-valued-bag(cs;C))))
Proof
Definitions occuring in Statement :
eclass2: (X o Y),
class-ap-val: X(v),
single-valued-classrel: single-valued-classrel(es;X;T),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type,
single-valued-bag: single-valued-bag(b;T),
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
single-valued-classrel: single-valued-classrel(es;X;T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
squash: ↓T,
exists: ∃x:A. B[x],
prop: ℙ,
rev_uimplies: rev_uimplies(P;Q),
cand: A c∧ B,
single-valued-bag: single-valued-bag(b;T),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X:EClass(B {}\mrightarrow{} bag(C))]. \mforall{}[Y:EClass(B)]. \mforall{}[es:EO+(Info)].
(single-valued-classrel(es;(X o Y);C)) supposing
(single-valued-classrel(es;X;B {}\mrightarrow{} bag(C)) and
single-valued-classrel(es;Y;B) and
(\mforall{}b:B. \mforall{}cs:bag(C). \mforall{}es:EO+(Info). \mforall{}e:E. (cs \mmember{} X(b)(e) {}\mRightarrow{} single-valued-bag(cs;C))))
Date html generated:
2016_05_16-PM-02_12_06
Last ObjectModification:
2016_01_17-PM-07_37_03
Theory : event-ordering
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