Nuprl Lemma : State2-functional
∀[Info,A1,A2,S:Type]. ∀[init:Id ⟶ S]. ∀[tr1:Id ⟶ A1 ⟶ S ⟶ S]. ∀[X1:EClass(A1)]. ∀[tr2:Id ⟶ A2 ⟶ S ⟶ S].
∀[X2:EClass(A2)].
∀es:EO+(Info)
(single-valued-classrel(es;X1;A1)
⇒ single-valued-classrel(es;X2;A2)
⇒ disjoint-classrel(es;A1;X1;A2;X2)
⇒ State2(init;tr1;X1;tr2;X2) is functional)
Proof
Definitions occuring in Statement :
State2: State2(init;tr1;X1;tr2;X2),
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,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
State2: State2(init;tr1;X1;tr2;X2),
uimplies: b supposing a,
top: Top,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ,
es-functional-class: X is functional,
single-valued-classrel: single-valued-classrel(es;X;T),
subtype_rel: A ⊆r B,
es-total-class: es-total-class(es;X),
nat: ℕ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A1,A2,S:Type]. \mforall{}[init:Id {}\mrightarrow{} S]. \mforall{}[tr1:Id {}\mrightarrow{} A1 {}\mrightarrow{} S {}\mrightarrow{} S]. \mforall{}[X1:EClass(A1)]. \mforall{}[tr2:Id
{}\mrightarrow{} A2
{}\mrightarrow{} S
{}\mrightarrow{} S].
\mforall{}[X2:EClass(A2)].
\mforall{}es:EO+(Info)
(single-valued-classrel(es;X1;A1)
{}\mRightarrow{} single-valued-classrel(es;X2;A2)
{}\mRightarrow{} disjoint-classrel(es;A1;X1;A2;X2)
{}\mRightarrow{} State2(init;tr1;X1;tr2;X2) is functional)
Date html generated:
2016_05_17-AM-10_05_20
Last ObjectModification:
2015_12_29-PM-03_52_20
Theory : classrel!lemmas
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