:: deftheorem defines turns_right GOBRD13:def 6 :
for D being set
for f being FinSequence of D
for G being Matrix of D
for k being Nat holds
( f turns_right k,G iff for i1, j1, i2, j2 being Nat st [i1,j1] in Indices G & [i2,j2] in Indices G & f /. k = G * (i1,j1) & f /. (k + 1) = G * (i2,j2) & not ( i1 = i2 & j1 + 1 = j2 & [(i2 + 1),j2] in Indices G & f /. (k + 2) = G * ((i2 + 1),j2) ) & not ( i1 + 1 = i2 & j1 = j2 & [i2,(j2 -' 1)] in Indices G & f /. (k + 2) = G * (i2,(j2 -' 1)) ) & not ( i1 = i2 + 1 & j1 = j2 & [i2,(j2 + 1)] in Indices G & f /. (k + 2) = G * (i2,(j2 + 1)) ) holds
( i1 = i2 & j1 = j2 + 1 & [(i2 -' 1),j2] in Indices G & f /. (k + 2) = G * ((i2 -' 1),j2) ) );