Nuprl Lemma : classfun-res-disjoint-union-comb-left
∀[Info,A,B:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[e:E].
(X (+) Y@e = (inl X@e) ∈ (A + B)) supposing
(single-valued-classrel(es;X;A) and
disjoint-classrel(es;A;X;B;Y) and
(↑e ∈b X))
Proof
Definitions occuring in Statement :
disjoint-union-comb: X (+) Y,
classfun-res: X@e,
single-valued-classrel: single-valued-classrel(es;X;T),
disjoint-classrel: disjoint-classrel(es;A;X;B;Y),
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
inl: inl x,
union: left + right,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
disjoint-union-comb: X (+) Y,
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uimplies: b supposing a,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
prop: ℙ,
not: ¬A,
false: False,
lifting-1: lifting-1(f),
lifting1: lifting1(f;b),
lifting-gen-rev: lifting-gen-rev(n;f;bags),
lifting-gen-list-rev: lifting-gen-list-rev(n;bags),
eq_int: (i =z j),
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
so_lambda: λ2x.t[x],
so_apply: x[s],
single-bag: {x},
bag-null: bag-null(bs),
top: Top,
assert: ↑b,
decidable: Dec(P),
or: P ∨ Q,
squash: ↓T,
exists: ∃x:A. B[x],
classfun-res: X@e,
simple-comb-1: F|X|,
classfun: X(e),
simple-comb: simple-comb(F;Xs),
select: L[n],
cons: [a / b],
eclass: EClass(A[eo; e]),
iff: P ⇐⇒ Q
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[e:E].
(X (+) Y@e = (inl X@e)) supposing
(single-valued-classrel(es;X;A) and
disjoint-classrel(es;A;X;B;Y) and
(\muparrow{}e \mmember{}\msubb{} X))
Date html generated:
2016_05_17-AM-11_16_13
Last ObjectModification:
2015_12_29-PM-05_13_04
Theory : process-model
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