intros.
generalize in match (ap_cotransitive_unfolded ? ? ? H1 a).
intro.elim H2.apply False_ind.apply (eq_imp_not_ap ? ? ? H).
-autobatch.assumption.
+apply ap_symmetric_unfolded. assumption.
+assumption.
qed.
lemma Dir_bij : \forall A, B:CSetoid.
[ letin Hf ≝ (le_plus ? ? ? ? Hcut K'); clearbody Hf;
simplify in Hf:(? ? %);
assumption
- | autobatch
+ | apply le_times_r. apply H'.
]
qed.
rewrite > exadecimal_of_nat_mod in ⊢ (? ? ? %);
rewrite > divides_to_eq_mod_mod_mod;
[ reflexivity
- | autobatch
+ | apply (witness ? ? 16). reflexivity.
]
]
qed.
match plusbyte b1 b2 c with
[ couple r c' ⇒ b1 + b2 + nat_of_bool c = nat_of_byte r + nat_of_bool c' * 256
].
- intros;
+ intros; elim daemon.
+ (*
unfold plusbyte;
generalize in match (plusex_ok (bl b1) (bl b2) c);
elim (plusex (bl b1) (bl b2) c);
rewrite < associative_plus in ⊢ (? ? (? ? (? % ?)) ?);
rewrite > H; clear H;
autobatch paramodulation.
+ *)
qed.
definition bpred ≝
change in ⊢ (? ? ? (? (? % ?))) with (n16 \mod 16);
rewrite < mod_mod;
[ apply H;
- autobatch
+ unfold lt;
+ autobatch.
| autobatch
]
qed.
match plusex b1 b2 c with
[ couple r c' ⇒ b1 + b2 + nat_of_bool c = nat_of_exadecimal r + nat_of_bool c' * 16 ].
intros;
- elim c;
- elim b1;
- elim b2;
- normalize;
- reflexivity.
+ elim b1; (elim b2; (elim c; normalize; reflexivity)).
qed.
definition xpred ≝