deffunc H₁( set , Function of (Inf_seq S),BOOLEAN , Function of (Inf_seq S),BOOLEAN ) -> Element of BOOLEAN = Until_univ $1,$2,$3,S;
for h1, h2 being set st h1 in ModelSP (Inf_seq S) & ( for t being set st t in Inf_seq S holds
( H₁(t, Fid f,(Inf_seq S), Fid g,(Inf_seq S)) = TRUE iff (Fid h1,(Inf_seq S)) . t = TRUE ) ) & h2 in ModelSP (Inf_seq S) & ( for t being set st t in Inf_seq S holds
( H₁(t, Fid f,(Inf_seq S), Fid g,(Inf_seq S)) = TRUE iff (Fid h2,(Inf_seq S)) . t = TRUE ) ) holds
h1 = h2 from MODELC_1:sch 7();
hence for b₁, b₂ being Element of ModelSP (Inf_seq S) st ( for t being set st t in Inf_seq S holds
( Until_univ t,(Fid f,(Inf_seq S)),(Fid g,(Inf_seq S)),S = TRUE iff (Fid b₁,(Inf_seq S)) . t = TRUE ) ) & ( for t being set st t in Inf_seq S holds
( Until_univ t,(Fid f,(Inf_seq S)),(Fid g,(Inf_seq S)),S = TRUE iff (Fid b₂,(Inf_seq S)) . t = TRUE ) ) holds
b₁ = b₂ ; :: thesis: verum