Nuprl Lemma : E-interface-pair
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X,Y:EClass(Top)]. E((X,Y)) = E(Y) ∈ Type supposing E(Y) ⊆r E(X)
Proof
Definitions occuring in Statement :
es-interface-pair: (X,Y),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
not: ¬A,
false: False,
assert: ↑b,
bnot: ¬bb,
guard: {T},
sq_type: SQType(T),
or: P ∨ Q,
exists: ∃x:A. B[x],
bfalse: ff,
prop: ℙ,
ifthenelse: if b then t else f fi ,
band: p ∧b q,
and: P ∧ Q,
uiff: uiff(P;Q),
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
implies: P ⇒ Q,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
es-E-interface: E(X),
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
true: True
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X,Y:EClass(Top)]. E((X,Y)) = E(Y) supposing E(Y) \msubseteq{}r E(X)
Date html generated:
2016_05_17-AM-08_10_57
Last ObjectModification:
2015_12_28-PM-11_11_57
Theory : event-ordering
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