Nuprl Lemma : es-interface-union-left
∀[Info,A:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(Top)]. left(X+Y) = X ∈ EClass(A) supposing Singlevalued(X)
Proof
Definitions occuring in Statement :
es-interface-union: X+Y,
es-interface-left: left(X),
sv-class: Singlevalued(X),
eclass: EClass(A[eo; e]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
eclass: EClass(A[eo; e]),
es-interface-union: X+Y,
es-interface-left: left(X),
eclass-compose2: eclass-compose2(f;X;Y),
eclass-compose1: f o X,
in-eclass: e ∈b X,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
top: Top,
eq_int: (i =z j),
bfalse: ff,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
prop: ℙ,
nat: ℕ,
cand: A c∧ B,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
single-bag: {x},
bag-only: only(bs),
bag-separate: bag-separate(bs),
pi1: fst(t),
bag-mapfilter: bag-mapfilter(f;P;bs),
bag-filter: [x∈b|p[x]],
bag-map: bag-map(f;bs),
isl: isl(x),
outl: outl(x),
empty-bag: {},
iff: P ⇐⇒ Q,
guard: {T},
rev_implies: P ⇐ Q
Latex:
\mforall{}[Info,A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(Top)]. left(X+Y) = X supposing Singlevalued(X)
Date html generated:
2016_05_16-PM-10_36_44
Last ObjectModification:
2016_01_17-PM-07_24_21
Theory : event-ordering
Home
Index