Nuprl Lemma : is-interface-part
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[T:Type]. ∀[X:EClass(T)]. ∀[g:E(X) ⟶ Id]. ∀[i:Id]. ∀[e:E].
uiff(↑e ∈b (X|g=i);(↑e ∈b X) ∧ ((g e) = i ∈ Id))
Proof
Definitions occuring in Statement :
es-interface-part: (X|g=i),
es-E-interface: E(X),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
in-eclass: e ∈b X,
es-interface-part: (X|g=i),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
let: let,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
exposed-it: exposed-it,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
assert: ↑b,
rev_uimplies: rev_uimplies(P;Q),
prop: ℙ,
true: True,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
false: False,
not: ¬A,
nat: ℕ,
eq_int: (i =z j)
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[g:E(X) {}\mrightarrow{} Id]. \mforall{}[i:Id]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} (X|g=i);(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} ((g e) = i))
Date html generated:
2016_05_16-PM-10_55_56
Last ObjectModification:
2015_12_29-AM-10_47_00
Theory : event-ordering
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