from research import *
s=begin(1042,'Independence changes with held source values','Are the centered and E-completed radius conditions still independent when175/147 are supplied?',{},['File60 §2.6','C1041'])
from covenant_model import *
v={k:F(x) for k,x in json.loads((ROOT/'model/covenant_source_inputs.json').read_text()).items()};rows=coefficient_matrix(claims,KEYS[:13]);lhs=[25*rows[7][j]-2*rows[6][j] for j in range(13)];rhs=[0]*13;rhs[12]=21;rhs[10]=-25
finish(s,{'identity':'25A8−2A7 = 21·Abraham_life−25·Jacob_life','held_rhs':21*v['L_A']-25*v['L_J'],'consequence':'with175/147 held, the two radius conditions are equivalent'},'The two radius conditions are independent only while the relevant lifespans vary. With source175 and147 held, one condition implies the other. Constraint counts must state their held premises.','Reduce the entire selected Covenant claim list to a precise row basis.',{'coefficient_identity':lhs==rhs,'source_rhs_zero':21*v['L_A']-25*v['L_J']==0})