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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
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],
class-ap-val: X(v),
class-ap: X(e),
all: ∀x:A. B[x],
eclass: EClass(A[eo; e]),
exists: ∃x:A. B[x],
cand: A c∧ B,
rev_uimplies: rev_uimplies(P;Q)
Latex:
\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:
2016_05_16-PM-02_08_00
Last ObjectModification:
2016_01_17-PM-07_38_39
Theory : event-ordering
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