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

for a2, a3 being Element of BOOLEAN st a2 = s . y & a3 = s . c holds

(Following s) . [<*y,c*>,'&'] = a2 '&' a3

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

let s be State of (MajorityCirc (x,y,c)); :: thesis: for a2, a3 being Element of BOOLEAN st a2 = s . y & a3 = s . c holds

(Following s) . [<*y,c*>,'&'] = a2 '&' a3

s . a is Element of BOOLEAN ;

hence for a2, a3 being Element of BOOLEAN st a2 = s . y & a3 = s . c holds

(Following s) . [<*y,c*>,'&'] = a2 '&' a3 by Lm2; :: thesis: verum

for a2, a3 being Element of BOOLEAN st a2 = s . y & a3 = s . c holds

(Following s) . [<*y,c*>,'&'] = a2 '&' a3

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

let s be State of (MajorityCirc (x,y,c)); :: thesis: for a2, a3 being Element of BOOLEAN st a2 = s . y & a3 = s . c holds

(Following s) . [<*y,c*>,'&'] = a2 '&' a3

s . a is Element of BOOLEAN ;

hence for a2, a3 being Element of BOOLEAN st a2 = s . y & a3 = s . c holds

(Following s) . [<*y,c*>,'&'] = a2 '&' a3 by Lm2; :: thesis: verum