>get slide
slide: x;(y;x)* = (x;y)*;x  (proved)

no tasks

>reset

current task:
T0:  |- x;(y;x)* = (x;y)*;x

>cite antisym

current task:
T1:  |- x;(y;x)* < (x;y)*;x

>cite *L

current task:
T3:  |- (x;y)*;x;y;x + x < (x;y)*;x

>foc

current task:
T3:  |- (x;y)*;x;y;x + x < (x;y)*;x

(x;y)*;x;y;x + x < (x;y)*;x
----------------

>d r

current task:
T3:  |- (x;y)*;x;y;x + x < (x;y)*;x

(x;y)*;x;y;x + x < (x;y)*;x
               -

>cite id.L r

current task:
T3:  |- (x;y)*;x;y;x + 1;x < (x;y)*;x

(x;y)*;x;y;x + 1;x < (x;y)*;x
               ---

>u

current task:
T3:  |- (x;y)*;x;y;x + 1;x < (x;y)*;x

(x;y)*;x;y;x + 1;x < (x;y)*;x
------------------

>cite distrR r

current task:
T3:  |- ((x;y)*;x;y + 1);x < (x;y)*;x

((x;y)*;x;y + 1);x < (x;y)*;x
------------------

>d

current task:
T3:  |- ((x;y)*;x;y + 1);x < (x;y)*;x

((x;y)*;x;y + 1);x < (x;y)*;x
----------------

>cite commut+ l

current task:
T3:  |- (1 + (x;y)*;x;y);x < (x;y)*;x

(1 + (x;y)*;x;y);x < (x;y)*;x
----------------

>unf

current task:
T3:  |- (1 + (x;y)*;x;y);x < (x;y)*;x

>cite mono.R

current task:
T4:  |- 1 + (x;y)*;x;y < (x;y)*

>cite =<

current task:
T5:  |- 1 + (x;y)*;x;y = (x;y)*

>cite unwindR
task completed

current task:
T2:  |- (x;y)*;x < x;(y;x)*

>cite *R

current task:
T6:  |- x;y;x;(y;x)* + x < x;(y;x)*

>foc

current task:
T6:  |- x;y;x;(y;x)* + x < x;(y;x)*

x;y;x;(y;x)* + x < x;(y;x)*
----------------

>d r

current task:
T6:  |- x;y;x;(y;x)* + x < x;(y;x)*

x;y;x;(y;x)* + x < x;(y;x)*
               -

>cite id.R r

current task:
T6:  |- x;y;x;(y;x)* + x;1 < x;(y;x)*

x;y;x;(y;x)* + x;1 < x;(y;x)*
               ---

>u

current task:
T6:  |- x;y;x;(y;x)* + x;1 < x;(y;x)*

x;y;x;(y;x)* + x;1 < x;(y;x)*
------------------

>cite distrL r

current task:
T6:  |- x;(y;x;(y;x)* + 1) < x;(y;x)*

x;(y;x;(y;x)* + 1) < x;(y;x)*
------------------

>d r

current task:
T6:  |- x;(y;x;(y;x)* + 1) < x;(y;x)*

x;(y;x;(y;x)* + 1) < x;(y;x)*
  ----------------

>cite commut+ l

current task:
T6:  |- x;(1 + y;x;(y;x)*) < x;(y;x)*

x;(1 + y;x;(y;x)*) < x;(y;x)*
  ----------------

>unf

current task:
T6:  |- x;(1 + y;x;(y;x)*) < x;(y;x)*

>cite mono.L

current task:
T8:  |- 1 + y;x;(y;x)* < (y;x)*

>cite =<

current task:
T9:  |- 1 + y;x;(y;x)* = (y;x)*

>cite unwindL
task completed

no tasks

>