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
Lemmas :
bag-member_wf,
exists_wf,
squash_wf,
class-ap_wf,
bag-combine_wf,
bag-map_wf,
uiff_wf,
classrel_wf,
eclass3_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
iff_transitivity,
iff_weakening_uiff,
bag-member-combine,
bag-member-map
\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:
2015_07_17-PM-00_37_31
Last ObjectModification:
2015_01_27-PM-11_15_30
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