Nuprl Lemma : interface-part-val
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[g:⋂es:EO+(Info). (E(X) ⟶ Id)]. ∀[i:Id]. ∀[es:EO+(Info)]. ∀[e:E].
(X|g=i)(e) ~ X(e) supposing ↑e ∈b (X|g=i)
Proof
Definitions occuring in Statement :
es-interface-part: (X|g=i),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
top: Top,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
not: ¬A,
false: False,
assert: ↑b,
bnot: ¬bb,
guard: {T},
sq_type: SQType(T),
or: P ∨ Q,
prop: ℙ,
exists: ∃x:A. B[x],
bfalse: ff,
ifthenelse: if b then t else f fi ,
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
implies: P ⇒ Q,
all: ∀x:A. B[x],
in-eclass: e ∈b X,
let: let,
es-interface-part: (X|g=i),
eclass-val: X(e),
and: P ∧ Q,
uiff: uiff(P;Q),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[g:\mcap{}es:EO+(Info). (E(X) {}\mrightarrow{} Id)]. \mforall{}[i:Id]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
(X|g=i)(e) \msim{} X(e) supposing \muparrow{}e \mmember{}\msubb{} (X|g=i)
Date html generated:
2016_05_17-AM-08_09_11
Last ObjectModification:
2015_12_28-PM-11_12_21
Theory : event-ordering
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