Nuprl Lemma : State2-state-class2
∀[Info,A1,A2,S:Type]. ∀[init:Id ⟶ S]. ∀[tr1:Id ⟶ A1 ⟶ S ⟶ S]. ∀[X1:EClass(A1)]. ∀[tr2:Id ⟶ A2 ⟶ S ⟶ S].
∀[X2:EClass(A2)].
(State2(init;tr1;X1;tr2;X2) = state-class2(init;tr1;X1;tr2;X2) ∈ EClass(S))
Proof
Definitions occuring in Statement :
State2: State2(init;tr1;X1;tr2;X2),
state-class2: state-class2(init;tr1;X1;tr2;X2),
eclass: EClass(A[eo; e]),
Id: Id,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
state-class2: state-class2(init;tr1;X1;tr2;X2),
State2: State2(init;tr1;X1;tr2;X2),
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
squash: ↓T,
true: True,
eclass: EClass(A[eo; e]),
eclass1: (f o X),
parallel-class: X || Y,
disjoint-union-comb: X (+) Y,
eclass-compose2: eclass-compose2(f;X;Y),
lifting-1: lifting-1(f),
simple-comb-1: F|X|,
lifting1: lifting1(f;b),
simple-comb: simple-comb(F;Xs),
select: L[n],
cons: [a / b],
lifting-gen-rev: lifting-gen-rev(n;f;bags),
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,
class-ap: X(e),
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
disjoint-union-tr: tr1 + tr2,
compose: f o g,
isl: isl(x),
outl: outl(x),
outr: outr(x),
prop: ℙ
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)].
(State2(init;tr1;X1;tr2;X2) = state-class2(init;tr1;X1;tr2;X2))
Date html generated:
2016_05_17-AM-10_05_37
Last ObjectModification:
2016_01_17-PM-11_03_20
Theory : classrel!lemmas
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