Commit a0ab0da3 authored by Guillaume Melquiond's avatar Guillaume Melquiond

Simplified proof.

parent 1c9be77b
......@@ -269,28 +269,13 @@ Proof.
intros x y Hx Hxy.
case (Z_lt_le_dec 0 x).
clear Hx. intros Hx.
assert (Hy: (y <> 0)%Z).
apply sym_not_eq.
apply Zlt_not_eq.
now apply Zlt_le_trans with x.
rewrite 2!digits_ln_beta.
destruct (ln_beta beta (Z2R x)) as (ex, Hex). simpl.
specialize (Hex (Rgt_not_eq _ _ (Z2R_lt _ _ Hx))).
destruct (ln_beta beta (Z2R y)) as (ey, Hey). simpl.
specialize (Hey (Z2R_neq _ _ Hy)).
eapply bpow_lt_bpow.
apply Rle_lt_trans with (1 := proj1 Hex).
apply Rle_lt_trans with (Rabs (Z2R y)).
rewrite Rabs_pos_eq.
apply Rle_trans with (Z2R y).
apply ln_beta_monotone.
now apply (Z2R_lt 0).
now apply Z2R_le.
apply RRle_abs.
apply (Z2R_le 0).
now apply Zlt_le_weak.
apply Hey.
exact Hy.
apply sym_not_eq.
now apply Zlt_not_eq.
apply Zgt_not_eq.
now apply Zlt_le_trans with x.
now apply Zgt_not_eq.
intros Hx'.
rewrite (Zle_antisym _ _ Hx' Hx).
apply digits_ge_0.
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