:: ALGSTR_2 semantic presentation

K99() is V129() V130() V131() V132() V133() V134() V135() M2(K19(K95()))

K95() is V129() V130() V131() V135() set

K19(K95()) is set

K96() is V129() V135() set

K97() is V129() V130() V131() V132() V135() set

K98() is V129() V130() V131() V132() V133() V135() set

K20(K96(),K96()) is set

K19(K20(K96(),K96())) is set

K20(K20(K96(),K96()),K96()) is set

K19(K20(K20(K96(),K96()),K96())) is set

K20(K95(),K95()) is set

K19(K20(K95(),K95())) is set

K20(K20(K95(),K95()),K95()) is set

K19(K20(K20(K95(),K95()),K95())) is set

K20(K97(),K97()) is set

K19(K20(K97(),K97())) is set

K20(K20(K97(),K97()),K97()) is set

K19(K20(K20(K97(),K97()),K97())) is set

K20(K98(),K98()) is set

K19(K20(K98(),K98())) is set

K20(K20(K98(),K98()),K98()) is set

K19(K20(K20(K98(),K98()),K98())) is set

K20(K99(),K99()) is set

K20(K20(K99(),K99()),K99()) is set

K19(K20(K20(K99(),K99()),K99())) is set

K94() is V129() V130() V131() V132() V133() V134() V135() set

K19(K94()) is set

K19(K99()) is set

1 is set

F_Real is non empty non degenerated left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict left_zeroed add-left-invertible add-right-invertible Loop-like Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr

K143() is V6() V18(K20(K95(),K95()),K95()) M2(K19(K20(K20(K95(),K95()),K95())))

K145() is V6() V18(K20(K95(),K95()),K95()) M2(K19(K20(K20(K95(),K95()),K95())))

0 is V21() V28() V29() V30() V31() V129() V130() V131() V132() V133() V134() M3(K95(),K99())

doubleLoopStr(# K95(),K143(),K145(),1,0 #) is strict doubleLoopStr

0. F_Real is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

the carrier of F_Real is V129() V130() V131() set

L is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

a is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

b is V21() V29() M2(K95())

c is V21() V29() M2(K95())

z is V21() V29() M2(K95())

b * z is V21() V29() M2(K95())

x is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

L * x is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

L * x is V21() V29() M2(K95())

L is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

a is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

b is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

L * b is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

L * b is V21() V29() M2(K95())

L is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

a is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

L * a is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

L * a is V21() V29() M2(K95())

b is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

L * b is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

L * b is V21() V29() M2(K95())

c is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

z is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

z * c is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

z * c is V21() V29() M2(K95())

x is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

x * c is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

x * c is V21() V29() M2(K95())

L is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

L * (0. F_Real) is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

L * (0. F_Real) is V21() V29() M2(K95())

a is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

(0. F_Real) * a is V21() V29() left_add-cancelable right_add-cancelable add-cancelable right_complementable M2( the carrier of F_Real)

(0. F_Real) * a is V21() V29() M2(K95())

L is non empty left_add-cancelable add-right-invertible addLoopStr

the carrier of L is set

a is left_add-cancelable M2( the carrier of L)

0. L is left_add-cancelable M2( the carrier of L)

b is left_add-cancelable M2( the carrier of L)

a + b is left_add-cancelable M2( the carrier of L)

c is left_add-cancelable M2( the carrier of L)

a + c is left_add-cancelable M2( the carrier of L)

L is non empty left_add-cancelable add-right-invertible addLoopStr

the carrier of L is set

a is left_add-cancelable M2( the carrier of L)

b is left_add-cancelable M2( the carrier of L)

(L,b) is left_add-cancelable M2( the carrier of L)

a + (L,b) is left_add-cancelable M2( the carrier of L)

L is non empty doubleLoopStr

the carrier of L is set

0. L is M2( the carrier of L)

1. L is M2( the carrier of L)

a is M2( the carrier of L)

a + (0. L) is M2( the carrier of L)

b is M2( the carrier of L)

c is M2( the carrier of L)

z is M2( the carrier of L)

c + z is M2( the carrier of L)

x is M2( the carrier of L)

(c + z) + x is M2( the carrier of L)

z + x is M2( the carrier of L)

c + (z + x) is M2( the carrier of L)

c

c

c

c

c

c

c

(1. L) * c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

(0. L) * c

c

c

c

c

c

c

c

(c

a is M2( the carrier of L)

(0. L) + a is M2( the carrier of L)

a + (0. L) is M2( the carrier of L)

a is M2( the carrier of L)

b is M2( the carrier of L)

c is M2( the carrier of L)

a + c is M2( the carrier of L)

c + b is M2( the carrier of L)

z is M2( the carrier of L)

a + z is M2( the carrier of L)

(0. L) + b is M2( the carrier of L)

a is M2( the carrier of L)

b is M2( the carrier of L)

c is M2( the carrier of L)

a + c is M2( the carrier of L)

c + a is M2( the carrier of L)

a is M2( the carrier of L)

b is M2( the carrier of L)

a + b is M2( the carrier of L)

c is M2( the carrier of L)

a + c is M2( the carrier of L)

z is M2( the carrier of L)

z + a is M2( the carrier of L)

(z + a) + b is M2( the carrier of L)

z + (a + c) is M2( the carrier of L)

(z + a) + c is M2( the carrier of L)

(0. L) + c is M2( the carrier of L)

a is M2( the carrier of L)

b is M2( the carrier of L)

b + a is M2( the carrier of L)

c is M2( the carrier of L)

c + a is M2( the carrier of L)

a + b is M2( the carrier of L)

a + c is M2( the carrier of L)

L is non empty left_add-cancelable right_add-cancelable add-cancelable almost_left_cancelable almost_right_cancelable almost_cancelable left_zeroed add-left-invertible add-right-invertible Loop-like almost_invertible multLoop_0-like Abelian right_zeroed unital right-distributive right_unital well-unital left_unital doubleLoopStr

the carrier of L is set

a is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

b is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,b) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

a * (L,b) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

a * b is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,(a * b)) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(a * b) + (a * (L,b)) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

b + (L,b) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

a * (b + (L,b)) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

0. L is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

a * (0. L) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

L is non empty left_add-cancelable add-right-invertible Abelian addLoopStr

the carrier of L is set

a is left_add-cancelable M2( the carrier of L)

(L,a) is left_add-cancelable M2( the carrier of L)

(L,(L,a)) is left_add-cancelable M2( the carrier of L)

(L,a) + a is left_add-cancelable M2( the carrier of L)

0. L is left_add-cancelable M2( the carrier of L)

L is non empty left_add-cancelable right_add-cancelable add-cancelable almost_left_cancelable almost_right_cancelable almost_cancelable left_zeroed add-left-invertible add-right-invertible Loop-like almost_invertible multLoop_0-like Abelian right_zeroed unital right-distributive right_unital well-unital left_unital doubleLoopStr

1. L is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

the carrier of L is set

(L,(1. L)) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,(1. L)) * (L,(1. L)) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

1_ L is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,(1. L)) * (1_ L) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,((L,(1. L)) * (1_ L))) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,(L,(1. L))) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

L is non empty left_add-cancelable right_add-cancelable add-cancelable almost_left_cancelable almost_right_cancelable almost_cancelable left_zeroed add-left-invertible add-right-invertible Loop-like almost_invertible multLoop_0-like Abelian right_zeroed unital right-distributive right_unital well-unital left_unital doubleLoopStr

the carrier of L is set

a is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

b is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

c is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,b,c) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,c) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

b + (L,c) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

a * (L,b,c) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

a * b is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

a * c is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,(a * b),(a * c)) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,(a * c)) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(a * b) + (L,(a * c)) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

a * (L,c) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(a * b) + (a * (L,c)) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

L is non empty doubleLoopStr

the carrier of L is set

0. L is M2( the carrier of L)

1. L is M2( the carrier of L)

a is M2( the carrier of L)

a + (0. L) is M2( the carrier of L)

b is M2( the carrier of L)

c is M2( the carrier of L)

z is M2( the carrier of L)

c + z is M2( the carrier of L)

x is M2( the carrier of L)

(c + z) + x is M2( the carrier of L)

z + x is M2( the carrier of L)

c + (z + x) is M2( the carrier of L)

c

c

c

c

c

c

c

(1. L) * c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

(0. L) * c

c

c

c

c

(c

c

c

(c

a is M2( the carrier of L)

b is M2( the carrier of L)

c is M2( the carrier of L)

c + a is M2( the carrier of L)

b + c is M2( the carrier of L)

z is M2( the carrier of L)

z + a is M2( the carrier of L)

b + (0. L) is M2( the carrier of L)

a is M2( the carrier of L)

(0. L) + a is M2( the carrier of L)

a + (0. L) is M2( the carrier of L)

a is M2( the carrier of L)

b is M2( the carrier of L)

a + b is M2( the carrier of L)

c is M2( the carrier of L)

a + c is M2( the carrier of L)

z is M2( the carrier of L)

z + a is M2( the carrier of L)

(z + a) + b is M2( the carrier of L)

z + (a + c) is M2( the carrier of L)

(z + a) + c is M2( the carrier of L)

(0. L) + c is M2( the carrier of L)

a is M2( the carrier of L)

b is M2( the carrier of L)

b + a is M2( the carrier of L)

c is M2( the carrier of L)

c + a is M2( the carrier of L)

z is M2( the carrier of L)

a + z is M2( the carrier of L)

b + (a + z) is M2( the carrier of L)

(c + a) + z is M2( the carrier of L)

c + (a + z) is M2( the carrier of L)

c + (0. L) is M2( the carrier of L)

a is M2( the carrier of L)

b is M2( the carrier of L)

c is M2( the carrier of L)

a + c is M2( the carrier of L)

c + b is M2( the carrier of L)

z is M2( the carrier of L)

a + z is M2( the carrier of L)

(0. L) + b is M2( the carrier of L)

L is non empty left_add-cancelable right_add-cancelable add-cancelable almost_left_cancelable almost_right_cancelable almost_cancelable left_zeroed add-left-invertible add-right-invertible Loop-like almost_invertible multLoop_0-like right_zeroed unital left-distributive right_unital well-unital left_unital doubleLoopStr

the carrier of L is set

a is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,a) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

b is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,a) * b is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

a * b is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,(a * b)) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(a * b) + ((L,a) * b) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

a + (L,a) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(a + (L,a)) * b is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

0. L is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(0. L) * b is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

L is non empty left_add-cancelable right_add-cancelable add-cancelable almost_left_cancelable almost_right_cancelable almost_cancelable left_zeroed add-left-invertible add-right-invertible Loop-like almost_invertible multLoop_0-like Abelian right_zeroed unital left-distributive right_unital well-unital left_unital doubleLoopStr

1. L is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

the carrier of L is set

(L,(1. L)) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,(1. L)) * (L,(1. L)) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

1_ L is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(1_ L) * (L,(1. L)) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,((1_ L) * (L,(1. L)))) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,(L,(1. L))) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

L is non empty left_add-cancelable right_add-cancelable add-cancelable almost_left_cancelable almost_right_cancelable almost_cancelable left_zeroed add-left-invertible add-right-invertible Loop-like almost_invertible multLoop_0-like right_zeroed unital left-distributive right_unital well-unital left_unital doubleLoopStr

the carrier of L is set

a is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

b is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,a,b) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,b) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

a + (L,b) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

c is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,a,b) * c is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

a * c is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

b * c is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,(a * c),(b * c)) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,(b * c)) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(a * c) + (L,(b * c)) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(L,b) * c is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

(a * c) + ((L,b) * c) is left_add-cancelable right_add-cancelable add-cancelable M2( the carrier of L)

L is non empty doubleLoopStr

the carrier of L is set

0. L is M2( the carrier of L)

1. L is M2( the carrier of L)

a is M2( the carrier of L)

a + (0. L) is M2( the carrier of L)

b is M2( the carrier of L)

c is M2( the carrier of L)

z is M2( the carrier of L)

c + z is M2( the carrier of L)

x is M2( the carrier of L)

(c + z) + x is M2( the carrier of L)

z + x is M2( the carrier of L)

c + (z + x) is M2( the carrier of L)

c

c

c

c

c

c

c

(1. L) * c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

c

(0. L) * c

c

c

c

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c

c

c

(c

c

c

c

c

(c

c

c

(c

a is M2( the carrier of L)

b is M2( the carrier of L)

c is M2( the carrier of L)

c + a is M2( the carrier of L)

b + c is M2( the carrier of L)

z is M2( the carrier of L)

z + a is M2( the carrier of L)

b + (0. L) is M2( the carrier of L)

a is M2( the carrier of L)

(0. L) + a is M2( the carrier of L)

a + (0. L) is M2( the carrier of L)

a is M2( the carrier of L)

b is M2( the carrier of L)

a + b is M2( the carrier of L)

c is M2( the carrier of L)

a + c is M2( the carrier of L)

z is M2( the carrier of L)

z + a is M2( the carrier of L)

(z + a) + b is M2( the carrier of L)

z + (a + c) is M2( the carrier of L)

(z + a) + c is M2( the carrier of L)

(0. L) + c is M2( the carrier of L)

a is M2( the carrier of L)

b is M2( the carrier of L)

b + a is M2( the carrier of L)

c is M2( the carrier of L)

c + a is M2( the carrier of L)

z is M2( the carrier of L)

a + z is M2( the carrier of L)

b + (a + z) is M2( the carrier of L)

(c + a) + z is M2( the carrier of L)

c + (a + z) is M2( the carrier of L)

c + (0. L) is M2( the carrier of L)

a is M2( the carrier of L)

b is M2( the carrier of L)

c is M2( the carrier of L)

a + c is M2( the carrier of L)

c + b is M2( the carrier of L)

z is M2( the carrier of L)

a + z is M2( the carrier of L)

(0. L) + b is M2( the carrier of L)

L is non empty doubleLoopStr

the carrier of L is set

0. L is M2( the carrier of L)

1. L is M2( the carrier of L)

a is M2( the carrier of L)

b is M2( the carrier of L)

a * b is M2( the carrier of L)

b * a is M2( the carrier of L)

c is M2( the carrier of L)

b * c is M2( the carrier of L)

(b * a) * (b * c) is M2( the carrier of L)

(b * a) * b is M2( the carrier of L)

((b * a) * b) * c is M2( the carrier of L)

b * (1. L) is M2( the carrier of L)

(b * (1. L)) * c is M2( the carrier of L)

L is non empty doubleLoopStr

the carrier of L is set

0. L is M2( the carrier of L)

1. L is M2( the carrier of L)

a is M2( the carrier of L)

(1. L) * a is M2( the carrier of L)

a * (1. L) is M2( the carrier of L)

b is M2( the carrier of L)

a * b is M2( the carrier of L)

b * a is M2( the carrier of L)

a * (b * a) is M2( the carrier of L)

L is non empty doubleLoopStr

0. L is M2( the carrier of L)

the carrier of L is set

1. L is M2( the carrier of L)

a is M2( the carrier of L)

b is M2( the carrier of L)

a * b is M2( the carrier of L)

b * a is M2( the carrier of L)

L is non empty doubleLoopStr

the carrier of L is set

0. L is M2( the carrier of L)

1. L is M2( the carrier of L)

a is M2( the carrier of L)

a + (0. L) is M2( the carrier of L)

b is M2( the carrier of L)

c is M2( the carrier of L)

z is M2( the carrier of L)

c + z is M2( the carrier of L)

x is M2( the carrier of L)

(c + z) + x is M2( the carrier of L)

z + x is M2( the carrier of L)

c + (z + x) is M2( the carrier of L)

c

c

c

c

c

c

c

c

c

c

(0. L) * c

c

c

c

c

(c

c

c

c

c

c

c

c

c

c

(c

c

c

c

c

(c

c

c

(c

a is M2( the carrier of L)

(0. L) + a is M2( the carrier of L)

a + (0. L) is M2( the carrier of L)

a is M2( the carrier of L)

b is M2( the carrier of L)

c is M2( the carrier of L)

a + c is M2( the carrier of L)

c + b is M2( the carrier of L)

z is M2( the carrier of L)

a + z is M2( the carrier of L)

(0. L) + b is M2( the carrier of L)

a is M2( the carrier of L)

b is M2( the carrier of L)

c is M2( the carrier of L)

c + a is M2( the carrier of L)

b + c is M2( the carrier of L)

z is M2( the carrier of L)

z + a is M2( the carrier of L)

b + (0. L) is M2( the carrier of L)

a is M2( the carrier of L)

b is M2( the carrier of L)

a + b is M2( the carrier of L)

c is M2( the carrier of L)

a + c is M2( the carrier of L)

z is M2( the carrier of L)

z + a is M2( the carrier of L)

(z + a) + b is M2( the carrier of L)

z + (a + c) is M2( the carrier of L)

(z + a) + c is M2( the carrier of L)

(0. L) + c is M2( the carrier of L)

a is M2( the carrier of L)

b is M2( the carrier of L)

b + a is M2( the carrier of L)

c is M2( the carrier of L)

c + a is M2( the carrier of L)

z is M2( the carrier of L)

a + z is M2( the carrier of L)

b + (a + z) is M2( the carrier of L)

(c + a) + z is M2( the carrier of L)

c + (a + z) is M2( the carrier of L)

c + (0. L) is M2( the carrier of L)

a is M2( the carrier of L)

(1. L) * a is M2( the carrier of L)

a * (1. L) is M2( the carrier of L)

a is M2( the carrier of L)

b is M2( the carrier of L)

c is M2( the carrier of L)

a * c is M2( the carrier of L)

c * b is M2( the carrier of L)

z is M2( the carrier of L)

a * z is M2( the carrier of L)

(1. L) * b is M2( the carrier of L)

a is M2( the carrier of L)

b is M2( the carrier of L)

c is M2( the carrier of L)

c * a is M2( the carrier of L)

b * c is M2( the carrier of L)

z is M2( the carrier of L)

z * a is M2( the carrier of L)

b * (1. L) is M2( the carrier of L)

a is M2( the carrier of L)

b is M2( the carrier of L)

a * b is M2( the carrier of L)

c is M2( the carrier of L)

a * c is M2( the carrier of L)

z is M2( the carrier of L)

z * a is M2( the carrier of L)

(z * a) * b is M2( the carrier of L)

z * (a * c) is M2( the carrier of L)

(z * a) * c is M2( the carrier of L)

(1. L) * c is M2( the carrier of L)

a is M2( the carrier of L)

b is M2( the carrier of L)

b * a is M2( the carrier of L)

c is M2( the carrier of L)

c * a is M2( the carrier of L)

z is M2( the carrier of L)

a * z is M2( the carrier of L)

b * (a * z) is M2( the carrier of L)

(c * a) * z is M2( the carrier of L)

c * (a * z) is M2( the carrier of L)

c * (1. L) is M2( the carrier of L)

L is non empty doubleLoopStr

the carrier of L is set

0. L is M2( the carrier of L)

1. L is M2( the carrier of L)

a is M2( the carrier of L)

a + (0. L) is M2( the carrier of L)

b is M2( the carrier of L)

c is M2( the carrier of L)

z is M2( the carrier of L)

c + z is M2( the carrier of L)

x is M2( the carrier of L)

(c + z) + x is M2( the carrier of L)

z + x is M2( the carrier of L)

c + (z + x) is M2( the carrier of L)

c

c

c

c

c

c

c

c

c

c

c

c

c

(c

c

c

c

c

c

c

c

c

c

(c

c

c

c

c

a is M2( the carrier of L)

(0. L) * a is M2( the carrier of L)

a * (0. L) is M2( the carrier of L)

a is M2( the carrier of L)

b is M2( the carrier of L)

b * a is M2( the carrier of L)

c is M2( the carrier of L)

b + c is M2( the carrier of L)

(b + c) * a is M2( the carrier of L)

c * a is M2( the carrier of L)

(b * a) + (c * a) is M2( the carrier of L)

a * (b + c) is M2( the carrier of L)

a * b is M2( the carrier of L)

a * c is M2( the carrier of L)

(a * b) + (a * c) is M2( the carrier of L)

(b * a) + (a * c) is M2( the carrier of L)