Nuprl Lemma : State3-loc-exists
∀[Info,A1,A2,A3,S:Type]. ∀[init:Id ⟶ S]. ∀[tr1:Id ⟶ A1 ⟶ S ⟶ S]. ∀[X1:EClass(A1)]. ∀[tr2:Id ⟶ A2 ⟶ S ⟶ S].
∀[X2:EClass(A2)]. ∀[tr3:Id ⟶ A3 ⟶ S ⟶ S]. ∀[X3:EClass(A3)].
∀es:EO+(Info). ∀e:E. (↓∃v:S. v ∈ State3(init;tr1;X1;tr2;X2;tr3;X3)(e))
Proof
Definitions occuring in Statement :
State3: State3(init;tr1;X1;tr2;X2;tr3;X3),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
State3: State3(init;tr1;X1;tr2;X2;tr3;X3),
implies: P ⇒ Q,
not: ¬A,
false: False,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bag-null: bag-null(bs),
null: null(as),
single-bag: {x},
cons: [a / b],
bfalse: ff,
prop: ℙ,
subtype_rel: A ⊆r B,
squash: ↓T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A1,A2,A3,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{}[tr3:Id {}\mrightarrow{} A3 {}\mrightarrow{} S {}\mrightarrow{} S]. \mforall{}[X3:EClass(A3)].
\mforall{}es:EO+(Info). \mforall{}e:E. (\mdownarrow{}\mexists{}v:S. v \mmember{} State3(init;tr1;X1;tr2;X2;tr3;X3)(e))
Date html generated:
2016_05_17-AM-10_06_05
Last ObjectModification:
2016_01_17-PM-11_05_26
Theory : classrel!lemmas
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