Nuprl Lemma : eclass3-classrel
∀[Info,B,C:Type]. ∀[X:EClass(B ⟶ C)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].
uiff(v ∈ eclass3(X;Y)(e);↓∃f:B ⟶ C. ∃b:B. (f ∈ X(e) ∧ b ∈ Y(e) ∧ (v = (f b) ∈ C)))
Proof
Definitions occuring in Statement :
eclass3: eclass3(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,
equal: s = t ∈ T
Definitions unfolded in proof :
classrel: v ∈ X(e),
eclass3: eclass3(X;Y),
class-ap: X(e),
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
squash: ↓T,
exists: ∃x:A. B[x],
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
cand: A c∧ B,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
bag-member: x ↓∈ bs,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
rev_implies: P ⇐ Q
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X:EClass(B {}\mrightarrow{} C)]. \mforall{}[Y:EClass(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:C].
uiff(v \mmember{} eclass3(X;Y)(e);\mdownarrow{}\mexists{}f:B {}\mrightarrow{} C. \mexists{}b:B. (f \mmember{} X(e) \mwedge{} b \mmember{} Y(e) \mwedge{} (v = (f b))))
Date html generated:
2016_05_16-PM-02_12_49
Last ObjectModification:
2016_01_17-PM-07_39_48
Theory : event-ordering
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