Nuprl Lemma : simple-loc-comb-2-concat-single-val
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A,B,C:Type]. ∀[F:Id ⟶ A ⟶ B ⟶ bag(C)]. ∀[X:EClass(A)]. ∀[Y:EClass(B)].
single-valued-classrel(es;F@Loc o (Loc,X, Y);C)
supposing (∀i:Id. ∀a:A. ∀b:B. (#(F i a b) ≤ 1)) ∧ single-valued-classrel(es;X;A) ∧ single-valued-classrel(es;Y;B)
Proof
Definitions occuring in Statement :
concat-lifting-loc-2: f@Loc,
simple-loc-comb-2: F o (Loc,X, Y),
single-valued-classrel: single-valued-classrel(es;X;T),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
all: ∀x:A. B[x],
and: P ∧ Q,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
bag-size: #(bs),
bag: bag(T)
Definitions unfolded in proof :
single-valued-classrel: single-valued-classrel(es;X;T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
prop: ℙ,
cand: A c∧ B,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B,C:Type]. \mforall{}[F:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} bag(C)]. \mforall{}[X:EClass(A)].
\mforall{}[Y:EClass(B)].
single-valued-classrel(es;F@Loc o (Loc,X, Y);C)
supposing (\mforall{}i:Id. \mforall{}a:A. \mforall{}b:B. (\#(F i a b) \mleq{} 1))
\mwedge{} single-valued-classrel(es;X;A)
\mwedge{} single-valued-classrel(es;Y;B)
Date html generated:
2016_05_17-AM-09_29_09
Last ObjectModification:
2016_01_17-PM-11_09_24
Theory : classrel!lemmas
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