Nuprl Lemma : simple-comb-2-concat-classrel-weak
∀[Info,A,B,C:Type]. ∀[f:A ─→ B ─→ bag(C)]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].
(v ∈ f@|X, Y|(e) ⇐⇒ ↓∃a:A. ∃b:B. (a ∈ X(e) ∧ b ∈ Y(e) ∧ v ↓∈ f a b))
Proof
Definitions occuring in Statement :
simple-comb-2: F|X, Y|,
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
squash: ↓T,
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
concat-lifting-2: f@,
bag-member: x ↓∈ bs,
bag: bag(T)
Lemmas :
simple-comb-2-concat-classrel,
classrel_wf,
simple-comb-2_wf,
concat-lifting-2_wf,
squash_wf,
exists_wf,
bag-member_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
bag_wf
Latex:
\mforall{}[Info,A,B,C:Type]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} bag(C)]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
\mforall{}[v:C].
(v \mmember{} f@|X, Y|(e) \mLeftarrow{}{}\mRightarrow{} \mdownarrow{}\mexists{}a:A. \mexists{}b:B. (a \mmember{} X(e) \mwedge{} b \mmember{} Y(e) \mwedge{} v \mdownarrow{}\mmember{} f a b))
Date html generated:
2015_07_22-PM-00_10_59
Last ObjectModification:
2015_01_28-AM-11_40_31
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