proposition: Lemma Bounded_M_nonzero_denum: forall a b c d r, Bounded_M ((a,b),(c,d))->(-1<=r<=1)%R->(c*r+d<>0)%R.
proof: Proof. intros a b c d r H_vanish Hr; destruct (Qtrichotomy_inf Zero d) as [[Hd|Hd]|Hd]; [ apply Rlt_not_eq'; apply Bounded_M_pos with a b; trivial | intros _; apply (Bounded_M_nonzero a b c d); auto | apply Rlt_not_eq; apply Bounded_M_neg with a b; trivial]. Qed.
imports: digits Raxioms RIneq QArithSternBrocot(R_addenda) Fourier_solvable_ineqs