for p, q being SCPartialNominativePredicate of V,A st dom p = ND (V,A) & ( for d being object st d in dom p holds
( ( S₁[d] implies p . d = TRUE ) & ( not S₁[d] implies p . d = FALSE ) ) ) & dom q = ND (V,A) & ( for d being object st d in dom q holds
( ( S₁[d] implies q . d = TRUE ) & ( not S₁[d] implies q . d = FALSE ) ) ) holds
p = q from PARTPR_2:sch 2();
hence for b₁, b₂ being SCPartialNominativePredicate of V,A st dom b₁ = ND (V,A) & ( for d being object st d in dom b₁ holds
( ( valid_power_input_pred V,A,val,b0,n0,d implies b₁ . d = TRUE ) & ( not valid_power_input_pred V,A,val,b0,n0,d implies b₁ . d = FALSE ) ) ) & dom b₂ = ND (V,A) & ( for d being object st d in dom b₂ holds
( ( valid_power_input_pred V,A,val,b0,n0,d implies b₂ . d = TRUE ) & ( not valid_power_input_pred V,A,val,b0,n0,d implies b₂ . d = FALSE ) ) ) holds
b₁ = b₂ ; :: thesis: verum