Nuprl Lemma : es-interface-part_wf
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[g:⋂es:EO+(Info). (E(X) ⟶ Id)]. ∀[i:Id]. ((X|g=i) ∈ EClass(T))
Proof
Definitions occuring in Statement :
es-interface-part: (X|g=i),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
uall: ∀[x:A]. B[x],
member: t ∈ T,
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
eclass: EClass(A[eo; e]),
es-interface-part: (X|g=i),
all: ∀x:A. B[x],
implies: P ⇒ Q,
let: let,
subtype_rel: A ⊆r B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
nat: ℕ,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
es-E-interface: E(X),
in-eclass: e ∈b X,
rev_uimplies: rev_uimplies(P;Q),
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
not: ¬A,
so_lambda: λ2x.t[x],
so_apply: x[s]
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[g:\mcap{}es:EO+(Info). (E(X) {}\mrightarrow{} Id)]. \mforall{}[i:Id]. ((X|g=i) \mmember{} EClass(T))
Date html generated:
2016_05_16-PM-10_55_40
Last ObjectModification:
2016_01_17-PM-07_17_09
Theory : event-ordering
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