Nuprl Lemma : classfun-res-eclass3
∀[Info,B,C:Type]. ∀[X:EClass(B ⟶ C)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E].
(eclass3(X;Y)@e = (X@e Y@e) ∈ C) supposing (X is functional at e and Y is functional at e)
Proof
Definitions occuring in Statement :
eclass3: eclass3(X;Y),
classfun-res: X@e,
es-functional-class-at: X is functional at e,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
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,
uimplies: b supposing a,
classfun-res: X@e,
eclass3: eclass3(X;Y),
classfun: X(e),
class-ap: X(e),
eclass: EClass(A[eo; e]),
so_lambda: λ2x.t[x],
so_apply: x[s],
es-functional-class-at: X is functional at e,
implies: P ⇒ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
top: Top,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
guard: {T},
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].
(eclass3(X;Y)@e = (X@e Y@e)) supposing (X is functional at e and Y is functional at e)
Date html generated:
2016_05_17-AM-11_16_34
Last ObjectModification:
2015_12_29-PM-05_13_37
Theory : process-model
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