Nuprl Lemma : is-interface-left
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top + Top)]. ∀[e:E]. uiff(↑e ∈b left(X);(↑e ∈b X) ∧ (↑isl(X(e))))
Proof
Definitions occuring in Statement :
es-interface-left: left(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
isl: isl(x),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
top: Top,
and: P ∧ Q,
union: left + right,
universe: Type
Definitions unfolded in proof :
eclass-val: X(e),
in-eclass: e ∈b X,
es-interface-left: left(X),
eclass-compose1: f o X,
member: t ∈ T,
eclass: EClass(A[eo; e]),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
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 ,
assert: ↑b,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
false: False,
eq_int: (i =z j),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
cand: A c∧ B,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
single-bag: {x},
bag-only: only(bs),
bag-separate: bag-separate(bs),
pi1: fst(t),
isl: isl(x),
bag-mapfilter: bag-mapfilter(f;P;bs),
bag-filter: [x∈b|p[x]],
bag-map: bag-map(f;bs),
bag-size: #(bs),
true: True
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top + Top)]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} left(X);(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (\muparrow{}isl(X(e))))
Date html generated:
2016_05_16-PM-10_35_03
Last ObjectModification:
2016_01_17-PM-07_22_02
Theory : event-ordering
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