>pub p* = (p p)*(1+p)
L0: p* = (p;p)*;(1 + p)  (1 task)

current task:
T0:  |- p* = (p;p)*;(1 + p)

>cite antisym

current task:
T1:  |- p* < (p;p)*;(1 + p)

>foc

current task:
T1:  |- p* < (p;p)*;(1 + p)

p* < (p;p)*;(1 + p)
--

>cite id.L r

current task:
T1:  |- 1;p* < (p;p)*;(1 + p)

1;p* < (p;p)*;(1 + p)
----

>unf

current task:
T1:  |- 1;p* < (p;p)*;(1 + p)

>cite *L

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

>foc

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

(p;p)*;(1 + p);p + 1 < (p;p)*;(1 + p)
--------------------

>d d

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

(p;p)*;(1 + p);p + 1 < (p;p)*;(1 + p)
--------------

>cite distrL l

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

((p;p)*;1 + (p;p)*;p);p + 1 < (p;p)*;(1 + p)
---------------------

>u

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

((p;p)*;1 + (p;p)*;p);p + 1 < (p;p)*;(1 + p)
-----------------------

>cite distrR l

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

(p;p)*;1;p + (p;p)*;p;p + 1 < (p;p)*;(1 + p)
-----------------------

>d d

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

(p;p)*;1;p + (p;p)*;p;p + 1 < (p;p)*;(1 + p)
--------

>cite id.R l

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

(p;p)*;p + (p;p)*;p;p + 1 < (p;p)*;(1 + p)
------

>u u r

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

(p;p)*;p + (p;p)*;p;p + 1 < (p;p)*;(1 + p)
           --------------

>cite unwindR l
citation does not apply

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

(p;p)*;p + (p;p)*;p;p + 1 < (p;p)*;(1 + p)
           --------------

>cite commut+
which side? l

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

(p;p)*;p + 1 + (p;p)*;p;p < (p;p)*;(1 + p)
           --------------

>cite unwindR l

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

(p;p)*;p + (p;p)* < (p;p)*;(1 + p)
           ------

>cite id.R r

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

(p;p)*;p + (p;p)*;1 < (p;p)*;(1 + p)
           --------

>u

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

(p;p)*;p + (p;p)*;1 < (p;p)*;(1 + p)
-------------------

>cite distrL r

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

(p;p)*;(p + 1) < (p;p)*;(1 + p)
--------------

>d r

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

(p;p)*;(p + 1) < (p;p)*;(1 + p)
       -------

>cite commut+
which side? l

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

(p;p)*;(1 + p) < (p;p)*;(1 + p)
       -------

>u

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

(p;p)*;(1 + p) < (p;p)*;(1 + p)
--------------

>unf

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

>cite ref<
task completed

current task:
T2:  |- (p;p)*;(1 + p) < p*

>pub 1 < x*
L1: 1 < x*  (1 task)

current task:
T4:  |- 1 < x*

>pub x < x*
L2: x < x*  (1 task)

current task:
T5:  |- x < x*

>pub x*x* < x*
L3: x*;x* < x*  (1 task)

current task:
T6:  |- x*;x* < x*

>pub x** < x*
L4: x** < x*  (1 task)

current task:
T7:  |- x** < x*

>pub x < z* -> y < z* -> x y < z*
L5: x < z* -> y < z* -> x;y < z*  (1 task)

current task:
T8: x < z*, y < z* |- x;y < z*

>lib
L5: x < z* -> y < z* -> x;y < z*  (1 task)
L4: x** < x*  (1 task)
L3: x*;x* < x*  (1 task)
L2: x < x*  (1 task)
L1: 1 < x*  (1 task)
L0: p* = (p;p)*;(1 + p)  (1 task)
ref=: x = x  (proved)
sym: x = y -> y = x  (proved)
trans=: x = y -> y = z -> x = z  (proved)
cong+R: x = y -> x + z = y + z  (proved)
cong.L: y = z -> x;y = x;z  (proved)
cong.R: x = y -> x;z = y;z  (proved)
cong*: x = y -> x* = y*  (proved)
<intro: x + y = y -> x < y  (proved)
<elim: x < y -> x + y = y  (proved)
ref<: x < x  (proved)
antisym: x < y -> y < x -> x = y  (proved)
trans<: x < y -> y < z -> x < z  (proved)
supL: x < x + y  (proved)
supR: y < x + y  (proved)
sup: x < z -> y < z -> x + y < z  (proved)
=<: x = y -> x < y  (proved)
mono+R: x < y -> x + z < y + z  (proved)
mono.L: y < z -> x;y < x;z  (proved)
mono.R: x < y -> x;z < y;z  (proved)
mono*: x < y -> x* < y*  (proved)
commut+: x + y = y + x  (proved)
id+L: 0 + x = x  (proved)
id+R: x + 0 = x  (proved)
idemp+: x + x = x  (proved)
id.L: 1;x = x  (proved)
id.R: x;1 = x  (proved)
annihL: 0;x = 0  (proved)
annihR: x;0 = 0  (proved)
distrL: x;(y + z) = x;y + x;z  (proved)
distrR: (x + y);z = x;z + y;z  (proved)
unwindL: 1 + x;x* = x*  (proved)
unwindR: 1 + x*;x = x*  (proved)
*L: z;y + x < z -> x;y* < z  (proved)
*R: x;z + y < z -> x*;y < z  (proved)
slide: x;(y;x)* = (x;y)*;x  (proved)
denest: x*;(y;x*)* = (x + y)*  (proved)
commut.: B;C = C;B  (proved)
idemp.: B;B = B  (proved)
~~: ~~B = B  (proved)
deMorgan+: ~(B + C) = ~B;~C  (proved)
deMorgan.: ~(B;C) = ~B + ~C  (proved)
~0: ~0 = 1  (proved)
~1: ~1 = 0  (proved)
compl+: B + ~B = 1  (proved)
compl.: B;~B = 0  (proved)
<1: B + 1 = 1  (proved)
distr.L: B + C;D = (B + C);(B + D)  (proved)
distr.R: B;C + D = (B + D);(C + D)  (proved)
abs+: B + B;C = B  (proved)
abs.: B;(B + C) = B  (proved)

current task:
T8: x < z*, y < z* |- x;y < z*

>get L0
L0: p* = (p;p)*;(1 + p)  (1 task)

current task:
T2:  |- (p;p)*;(1 + p) < p*

>cite L5

current task:
T9:  |- (p;p)* < p*

>cite trans<
y=? p**

current task:
T11:  |- (p;p)* < p**

>cite mono*

current task:
T13:  |- p;p < p*

>cite L5

current task:
T14:  |- p < p*

>cite L2
task completed

current task:
T15:  |- p < p*

>cite L2
task completed

current task:
T12:  |- p** < p*

>cite L4
task completed

current task:
T10:  |- 1 + p < p*

>cite sup

current task:
T16:  |- 1 < p*

>cite L1
task completed

current task:
T17:  |- p < p*

>cite L2
task completed

no tasks

>get L1
L1: 1 < x*  (1 task)

current task:
T4:  |- 1 < x*

>cite trans<
y=? 1 + x x*

current task:
T18:  |- 1 < 1 + x;x*

>cite supL
task completed

current task:
T19:  |- 1 + x;x* < x*

>cite =<

current task:
T20:  |- 1 + x;x* = x*

>cite unwindL
task completed

no tasks

>get L2
L2: x < x*  (1 task)

current task:
T5:  |- x < x*

>focus

current task:
T5:  |- x < x*

x < x*
-

>r

current task:
T5:  |- x < x*

x < x*
    --

>cite unwindL r

current task:
T5:  |- x < 1 + x;x*

x < 1 + x;x*
    --------

>d r d r

current task:
T5:  |- x < 1 + x;x*

x < 1 + x;x*
          --

>cite unwindL r

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

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

>cite commut+ l

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

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

>u

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

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

>cite distrL l

current task:
T5:  |- x < 1 + x;x;x* + x;1

x < 1 + x;x;x* + x;1
        ------------

>d r

current task:
T5:  |- x < 1 + x;x;x* + x;1

x < 1 + x;x;x* + x;1
                 ---

>cite id.R l

current task:
T5:  |- x < 1 + x;x;x* + x

x < 1 + x;x;x* + x
                 -

>unf

current task:
T5:  |- x < 1 + x;x;x* + x

>cite supR
task completed

no tasks

>get L3
L3: x*;x* < x*  (1 task)

current task:
T6:  |- x*;x* < x*

>cite *R

current task:
T35:  |- x;x* + x* < x*

>cite trans<
y=? 1 + x x* + x*

current task:
T36:  |- x;x* + x* < 1 + x;x* + x*

>cite supR
task completed

current task:
T37:  |- 1 + x;x* + x* < x*

>cite =<

current task:
T38:  |- 1 + x;x* + x* = x*

>cite <elim

current task:
T39:  |- 1 + x;x* < x*

>cite =<

current task:
T40:  |- 1 + x;x* = x*

>cite unwindL
task completed

no tasks

>get L4
L4: x** < x*  (1 task)

current task:
T7:  |- x** < x*

>foc

current task:
T7:  |- x** < x*

x** < x*
---

>cite id.R r

current task:
T7:  |- x**;1 < x*

x**;1 < x*
-----

>unf

current task:
T7:  |- x**;1 < x*

>cite *R

current task:
T41:  |- x*;x* + 1 < x*

>cite sup

current task:
T42:  |- x*;x* < x*

>cite L3
task completed

current task:
T43:  |- 1 < x*

>cite L1
task completed

no tasks

>get L5
L5: x < z* -> y < z* -> x;y < z*  (1 task)

current task:
T8: x < z*, y < z* |- x;y < z*

>cite trans<
y=? z*z*

current task:
T44: x < z*, y < z* |- x;y < z*;z*

>cite trans<
y=? x z*

current task:
T46: x < z*, y < z* |- x;y < x;z*

>cite mono.L

current task:
T48: x < z*, y < z* |- y < z*

>use A1
task completed

current task:
T47: x < z*, y < z* |- x;z* < z*;z*

>cite mono.R

current task:
T49: x < z*, y < z* |- x < z*

>use A0
task completed

current task:
T45: x < z*, y < z* |- z*;z* < z*

>cite L3
task completed

no tasks

>