Nuprl Lemma : simple-comb-2-concat-classrel
∀[Info,A,B,C:Type]. ∀[f:A ⟶ B ⟶ bag(C)]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].
uiff(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,
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,
concat-lifting-2: f@,
bag-member: x ↓∈ bs,
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,
concat-lifting-2: f@,
simple-comb-2: F|X, Y|,
simple-comb2: λx,y.F[x; y]|X;Y|,
squash: ↓T,
prop: ℙ,
all: ∀x:A. B[x],
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
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].
uiff(v \mmember{} f@|X, Y|(e);\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:
2016_05_17-AM-09_20_42
Last ObjectModification:
2016_01_17-PM-11_12_26
Theory : classrel!lemmas
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