Nuprl Lemma : es-interface-left-as-image
∀[Info,A,B:Type]. ∀[X:EClass(A + B)]. (left(X) = λx.case x of inl(a) => {a} | inr(b) => {}[X] ∈ EClass(A))
Proof
Definitions occuring in Statement :
es-interface-left: left(X),
es-filter-image: f[X],
eclass: EClass(A[eo; e]),
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
union: left + right,
universe: Type,
equal: s = t ∈ T,
single-bag: {x},
empty-bag: {}
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
es-filter-image: f[X],
es-interface-left: left(X),
eclass: EClass(A[eo; e]),
eclass-compose1: f o X,
eclass-val: X(e),
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,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
top: Top,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
single-bag: {x},
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: {}
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A + B)]. (left(X) = \mlambda{}x.case x of inl(a) => \{a\} | inr(b) => \{\}[X])
Date html generated:
2016_05_17-AM-06_49_33
Last ObjectModification:
2015_12_29-AM-00_23_44
Theory : event-ordering
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