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