Nuprl Lemma : memory-class3-functional
∀[Info,A1,A2,A3,B:Type]. ∀[init:Id ⟶ B]. ∀[tr1:Id ⟶ A1 ⟶ B ⟶ B]. ∀[X1:EClass(A1)]. ∀[tr2:Id ⟶ A2 ⟶ B ⟶ B].
∀[X2:EClass(A2)]. ∀[tr3:Id ⟶ A3 ⟶ B ⟶ B]. ∀[X3:EClass(A3)]. ∀[es:EO+(Info)].
(memory-class3(init;tr1;X1;tr2;X2;tr3;X3) is functional) supposing
(single-valued-classrel(es;X1;A1) and
single-valued-classrel(es;X2;A2) and
single-valued-classrel(es;X3;A3) and
disjoint-classrel(es;A1;X1;A2;X2) and
disjoint-classrel(es;A1;X1;A3;X3) and
disjoint-classrel(es;A2;X2;A3;X3))
Proof
Definitions occuring in Statement :
memory-class3: memory-class3(init;tr1;X1;tr2;X2;tr3;X3),
es-functional-class: X is functional,
single-valued-classrel: single-valued-classrel(es;X;T),
disjoint-classrel: disjoint-classrel(es;A;X;B;Y),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
memory-class3: memory-class3(init;tr1;X1;tr2;X2;tr3;X3),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uimplies: b supposing a,
top: Top,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
es-functional-class: X is functional,
single-valued-classrel: single-valued-classrel(es;X;T),
es-total-class: es-total-class(es;X)
Latex:
\mforall{}[Info,A1,A2,A3,B:Type]. \mforall{}[init:Id {}\mrightarrow{} B]. \mforall{}[tr1:Id {}\mrightarrow{} A1 {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X1:EClass(A1)]. \mforall{}[tr2:Id
{}\mrightarrow{} A2
{}\mrightarrow{} B
{}\mrightarrow{} B].
\mforall{}[X2:EClass(A2)]. \mforall{}[tr3:Id {}\mrightarrow{} A3 {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X3:EClass(A3)]. \mforall{}[es:EO+(Info)].
(memory-class3(init;tr1;X1;tr2;X2;tr3;X3) is functional) supposing
(single-valued-classrel(es;X1;A1) and
single-valued-classrel(es;X2;A2) and
single-valued-classrel(es;X3;A3) and
disjoint-classrel(es;A1;X1;A2;X2) and
disjoint-classrel(es;A1;X1;A3;X3) and
disjoint-classrel(es;A2;X2;A3;X3))
Date html generated:
2016_05_17-AM-10_06_53
Last ObjectModification:
2015_12_29-PM-03_52_44
Theory : classrel!lemmas
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