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Thomas Baruchel 2023-01-21 20:41:23 +01:00
parent b95fe2fb75
commit 6507761b38
1 changed files with 39 additions and 1 deletions
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src/thue_morse3.v
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@ -595,14 +595,52 @@ Proof.
(T F) | T F T F || F T F T | (T F) diff + impossible à gauche
*)
assert ({b=b1} + {~ b=b1}). apply bool_dec. destruct H1. rewrite e in H.
(*
assert (b2 = b0). destruct (b2); destruct b1; destruct b0.
reflexivity. contradiction n0. reflexivity. reflexivity.
contradiction n1. reflexivity. contradiction n1. reflexivity.
reflexivity. contradiction n0. reflexivity. reflexivity. rewrite H1 in H.
*)
(* cas b = b1 T F T F || F T F T *)
rewrite app_removelast_last with (l := b3::hd) (d := false) in H.
rewrite <- app_assoc in H.
assert ({last (b3::hd) false=b0} + {~ last (b3::hd) false=b0}).
apply bool_dec. destruct H1. rewrite e0 in H.
(* problème à gauche *)
destruct M. left. assumption. (* ici on postule le modulo = 2 *)
rewrite app_removelast_last with (l := b3::hd) (d := false) in Q.
rewrite last_length in Q. rewrite Nat.even_succ in Q. apply odd_mod4 in Q.
destruct Q.
assert (exists x, firstn 2 [b0;b1;b0;b1] = [x;x]). generalize H2.
assert (length [b0;b1;b0;b1] = 4). reflexivity. generalize H3.
replace (
removelast (b3 :: hd) ++
[b0] ++ b1 :: b0 :: b1 :: b2 :: b2 :: b1 :: b0 :: b1 :: b4 :: tl )
with (
removelast (b3 :: hd) ++ [b0;b1;b0;b1]
++ (b2 :: b2 :: b1 :: b0 :: b1 :: b4 :: tl )) in H.
generalize H. apply tm_step_factor4_1mod4. reflexivity.
destruct H3. inversion H3. rewrite <- H6 in H5. rewrite H5 in n1.
contradiction n1. reflexivity.
assert (exists x, skipn 2 [b0;b1;b0;b1] = [x;x]). generalize H2.
assert (length [b0;b1;b0;b1] = 4). reflexivity. generalize H3.
replace (
removelast (b3 :: hd) ++
[b0] ++ b1 :: b0 :: b1 :: b2 :: b2 :: b1 :: b0 :: b1 :: b4 :: tl )
with (
removelast (b3 :: hd) ++ [b0;b1;b0;b1]
++ (b2 :: b2 :: b1 :: b0 :: b1 :: b4 :: tl )) in H.
generalize H. apply tm_step_factor4_3mod4. reflexivity.
destruct H3. inversion H3. rewrite <- H6 in H5. rewrite H5 in n1.
contradiction n1. reflexivity. easy.
(* nouveau cas : last (b3 :: hd) false <> b0
(F T) | T F T F || F T F T | (F T) diff + impossible à droite
(F T) | T F T F || F T F T | (T F) 4n+2 a/rev a/a possible ?
*)