Nuprl Lemma : simple-loc-comb-3-concat-es-sv
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A,B,C:Type]. ∀[F:Id ⟶ A ⟶ B ⟶ C ⟶ bag(Top)]. ∀[X:EClass(A)]. ∀[Y:EClass(B)].
∀[Z:EClass(C)].
es-sv-class(es;concat-lifting-loc-3(F)|Loc, X, Y, Z|)
supposing (∀i:Id. ∀a:A. ∀b:B. ∀c:C. (#(F i a b c) ≤ 1)) ∧ es-sv-class(es;X) ∧ es-sv-class(es;Y) ∧ es-sv-class(es;Z)
Proof
Definitions occuring in Statement :
concat-lifting-loc-3: concat-lifting-loc-3(f),
simple-loc-comb-3: F|Loc, X, Y, Z|,
es-sv-class: es-sv-class(es;X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
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 :
concat-lifting-loc-3: concat-lifting-loc-3(f),
simple-loc-comb-3: F|Loc, X, Y, Z|,
es-sv-class: es-sv-class(es;X),
simple-loc-comb: F|Loc; Xs|,
select: L[n],
cons: [a / b],
subtract: n - m,
concat-lifting-loc: concat-lifting-loc(n;bags;loc;f),
concat-lifting: concat-lifting(n;f;bags),
concat-lifting-list: concat-lifting-list(n;bags),
and: P ∧ Q,
all: ∀x:A. B[x],
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,
member: t ∈ T,
uall: ∀[x:A]. B[x],
eclass: EClass(A[eo; e]),
subtype_rel: A ⊆r B,
nat: ℕ,
implies: P ⇒ Q,
decidable: Dec(P),
or: P ∨ Q,
guard: {T},
prop: ℙ,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s],
le: A ≤ B,
less_than': less_than'(a;b),
cand: A c∧ B,
empty-bag: {},
single-bag: {x},
bag-union: bag-union(bbs),
bag-size: #(bs),
concat: concat(ll),
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B,C:Type]. \mforall{}[F:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} C {}\mrightarrow{} bag(Top)]. \mforall{}[X:EClass(A)].
\mforall{}[Y:EClass(B)]. \mforall{}[Z:EClass(C)].
es-sv-class(es;concat-lifting-loc-3(F)|Loc, X, Y, Z|)
supposing (\mforall{}i:Id. \mforall{}a:A. \mforall{}b:B. \mforall{}c:C. (\#(F i a b c) \mleq{} 1))
\mwedge{} es-sv-class(es;X)
\mwedge{} es-sv-class(es;Y)
\mwedge{} es-sv-class(es;Z)
Date html generated:
2016_05_17-AM-09_29_04
Last ObjectModification:
2016_01_17-PM-11_11_29
Theory : classrel!lemmas
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