lemma divides_to_gcd_aux: ∀p,m,n. O < p → O < n →n ∣ m →
gcd_aux p m n = n.
-#p #m #n #posp @(lt_O_n_elim … posp) #l #posn #divnm normalize
+#p #m #n #posp @(lt_O_n_elim … posp) #l #posn #divnm whd in ⊢ (??%?)
>divides_to_dividesb_true normalize //
qed.
lemma not_divides_to_gcd_aux: ∀p,m,n. 0 < n → n ∤ m →
gcd_aux (S p) m n = gcd_aux p n (m \mod n).
-#p #m #n #lenm #divnm normalize >not_divides_to_dividesb_false
+#p #m #n #lenm #divnm whd in ⊢ (??%?) >not_divides_to_dividesb_false
normalize // qed.
theorem divides_gcd_aux_mn: ∀p,m,n. O < n → n ≤ m → n ≤ p →