Nuprl Lemma : eclass2-eclass1-classrel
∀[Info,A,B,C:Type]. ∀[f:Id ⟶ A ⟶ B ⟶ bag(C)]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].
uiff(v ∈ ((f o X) o Y)(e);↓∃a:A. ∃b:B. (a ∈ X(e) ∧ b ∈ Y(e) ∧ v ↓∈ f loc(e) a b))
Proof
Definitions occuring in Statement :
eclass2: (X o Y),
eclass1: (f o X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
and: P ∧ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
exists: ∃x:A. B[x],
uiff: uiff(P;Q),
uimplies: b supposing a,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
squash: ↓T,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
hint: hint(t),
true: True,
cand: A c∧ B
Latex:
\mforall{}[Info,A,B,C:Type]. \mforall{}[f:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} bag(C)]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[es:EO+(Info)].
\mforall{}[e:E]. \mforall{}[v:C].
uiff(v \mmember{} ((f o X) o Y)(e);\mdownarrow{}\mexists{}a:A. \mexists{}b:B. (a \mmember{} X(e) \mwedge{} b \mmember{} Y(e) \mwedge{} v \mdownarrow{}\mmember{} f loc(e) a b))
Date html generated:
2016_05_16-PM-02_11_52
Last ObjectModification:
2016_01_17-PM-07_43_19
Theory : event-ordering
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