Nuprl Lemma : classfun-res-eclass1
∀[Info,B,C:Type]. ∀[X:EClass(B)]. ∀[f:Id ⟶ B ⟶ C]. ∀[es:EO+(Info)]. ∀[e:E].
((f o X)@e = (f loc(e) X@e) ∈ C) supposing (single-valued-classrel(es;X;B) and (↑e ∈b X))
Proof
Definitions occuring in Statement :
eclass1: (f o X),
classfun-res: X@e,
single-valued-classrel: single-valued-classrel(es;X;T),
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
assert: ↑b,
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,
eclass1: (f o X),
classfun: X(e),
class-ap: X(e),
subtype_rel: A ⊆r B,
eclass: EClass(A[eo; e]),
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X:EClass(B)]. \mforall{}[f:Id {}\mrightarrow{} B {}\mrightarrow{} C]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
((f o X)@e = (f loc(e) X@e)) supposing (single-valued-classrel(es;X;B) and (\muparrow{}e \mmember{}\msubb{} X))
Date html generated:
2016_05_17-AM-11_16_27
Last ObjectModification:
2015_12_29-PM-05_11_43
Theory : process-model
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