let x, y, c be non pair object ; :: thesis: for s being State of (MajorityCirc (x,y,c))

for a1, a3 being Element of BOOLEAN st a1 = s . x & a3 = s . c holds

(Following s) . [<*c,x*>,'&'] = a3 '&' a1

reconsider a = y as Vertex of (MajorityStr (x,y,c)) by Th72;

let s be State of (MajorityCirc (x,y,c)); :: thesis: for a1, a3 being Element of BOOLEAN st a1 = s . x & a3 = s . c holds

(Following s) . [<*c,x*>,'&'] = a3 '&' a1

s . a is Element of BOOLEAN ;

hence for a1, a3 being Element of BOOLEAN st a1 = s . x & a3 = s . c holds

(Following s) . [<*c,x*>,'&'] = a3 '&' a1 by Lm2; :: thesis: verum

for a1, a3 being Element of BOOLEAN st a1 = s . x & a3 = s . c holds

(Following s) . [<*c,x*>,'&'] = a3 '&' a1

reconsider a = y as Vertex of (MajorityStr (x,y,c)) by Th72;

let s be State of (MajorityCirc (x,y,c)); :: thesis: for a1, a3 being Element of BOOLEAN st a1 = s . x & a3 = s . c holds

(Following s) . [<*c,x*>,'&'] = a3 '&' a1

s . a is Element of BOOLEAN ;

hence for a1, a3 being Element of BOOLEAN st a1 = s . x & a3 = s . c holds

(Following s) . [<*c,x*>,'&'] = a3 '&' a1 by Lm2; :: thesis: verum