Nuprl Lemma : class-ap-val-classrel
∀[Info,A,B:Type]. ∀[X:EClass(A ─→ B)]. ∀[a:A]. ∀[b:B]. ∀[es:EO+(Info)]. ∀[e:E].
uiff(b ∈ X(a)(e);↓∃f:A ─→ B. ((b = (f a) ∈ B) ∧ f ∈ X(e)))
Proof
Definitions occuring in Statement :
class-ap-val: X(v),
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 :
classrel_wf,
class-ap-val_wf,
squash_wf,
exists_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
bag-member-map
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A {}\mrightarrow{} B)]. \mforall{}[a:A]. \mforall{}[b:B]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
uiff(b \mmember{} X(a)(e);\mdownarrow{}\mexists{}f:A {}\mrightarrow{} B. ((b = (f a)) \mwedge{} f \mmember{} X(e)))
Date html generated:
2015_07_17-PM-00_34_50
Last ObjectModification:
2015_01_27-PM-11_32_47
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