-split;
-[1: cases Hx; cases H3; cases Hy; cases H7; split;
- [1: apply (le_transitive ???? (H8 0)); cases (Hyi 0); assumption
- |2: apply (le_transitive ????? (H4 0)); cases (Hxi 0); assumption]
-|2: intros 3;
- lapply (uparrow_upperlocated ? xi x Hx)as Ux;
- lapply (downarrow_lowerlocated ? yi x Hy)as Uy;
- letin Xi ≝ (⌊n,〈xi n,Hxi n〉⌋);
- letin Yi ≝ (⌊n,〈yi n,Hyi n〉⌋);
- letin Ai ≝ (⌊n,〈a n,H1 n〉⌋);
- apply (sandwich {[l,u]} 〈x,h〉 Xi Yi Ai); try assumption;
- [1: intro j; cases (Hxy j); cases H3; cases H4; split;
- [apply (H5 0);|apply (H7 0)]
- |2: cases (restrict_uniform_convergence_uparrow ? S ?? (H l u) Xi x Hx);
- apply (H4 h);
- |3: cases (restrict_uniform_convergence_downarrow ? S ?? (H l u) Yi x Hy);
- apply (H4 h);]]
+letin Xi ≝ (⌊n,≪xi n, Hxi n≫⌋);
+letin Yi ≝ (⌊n,≪yi n, Hyi n≫⌋);
+cases (restrict_uniform_convergence_uparrow ? S ?? (H l u) Xi x Hx);
+cases (restrict_uniform_convergence_downarrow ? S ?? (H l u) Yi x Hy);
+split; [1: assumption]
+intros 3;
+lapply (uparrow_upperlocated ? xi x Hx)as Ux;
+lapply (downarrow_lowerlocated ? yi x Hy)as Uy;
+letin Ai ≝ (⌊n,≪a n, H1 n≫⌋);
+apply (sandwich {[l,u]} ≪?, h≫ Xi Yi Ai); [4: assumption;|2:apply H3;|3:apply H5]
+intro j; cases (Hxy j); cases H7; cases H8; split; [apply (H9 0);|apply (H11 0)]