unfold.unfold.intros 2.elim x 2.elim y 2.
simplify.
intro.
-reduce in H2.
+normalize in H2.
apply (un_op_wd_unfolded ? f ? ? H2).
qed.
\forall f: CSetoid_un_op S. \forall pr: un_op_pres_pred S P f.
un_op_strext (mk_SubCSetoid S P) (restr_un_op S P f pr).
intros.unfold.unfold. intros 2.elim y 2. elim x 2.
-intros.reduce in H2.
+intros.normalize in H2.
apply (cs_un_op_strext ? f ? ? H2).
qed.
unfold.unfold.intros 2.elim x1 2. elim x2 2.intros 2. elim y1 2. elim y2 2.
simplify.
intros.
-reduce in H4.
-reduce in H5.
+normalize in H4.
+normalize in H5.
apply (cs_bin_op_wd ? f ? ? ? ? H4 H5).
qed.
bin_op_strext (mk_SubCSetoid S P) (restr_bin_op S P f pr).
intros.unfold.unfold. intros 2.elim x1 2. elim x2 2.intros 2. elim y1 2. elim y2 2.
simplify.intros.
-reduce in H4.
+normalize in H4.
apply (cs_bin_op_strext ? f ? ? ? ? H4).
qed.
fold simplify (sort nat_eqType); (* CANONICAL?! *)
cases (in_sub_eq nat_eqType (λx:nat_eqType.ltb x bound) w);
simplify; [2: reflexivity]
- generalize in match H1; clear H1; cases s; clear s; intros (H1);
- unfold segment; simplify; simplify in H1; rewrite > H1;
+ generalize in match H1; clear H1; cases s (r Pr); clear s; intros (H1);
+ unfold fsort; unfold segment; simplify; simplify in H1; rewrite > H1;
rewrite > iota_ltb in Hw; apply (p2bF ? ? (eqP nat_eqType ? ?));
unfold Not; intros (Enw); rewrite > Enw in Hw;
rewrite > ltb_refl in Hw; destruct Hw]
[ assumption
| assumption
]
- | rewrite > H14.
+ | unfold ha.
+ unfold ha12.
+ unfold ha22.
+ rewrite > H14.
rewrite > H13.
apply sym_eq.
apply div_mod.
rewrite > Hcut.
assumption
]
- | rewrite > Hcut1.
+ | unfold ha.
+ unfold ha12.
+ rewrite > Hcut1.
rewrite > Hcut.
assumption
]
- | rewrite > Hcut1.
+ | unfold ha.
+ unfold ha22.
+ rewrite > Hcut1.
rewrite > Hcut.
assumption
]
| cut(O \lt m1)
[ cut(O \lt n1)
[ apply (lt_to_le_to_lt ? ((h11 i j)*m1 + m1) )
- [ apply (lt_plus_r).
+ [ unfold ha.
+ apply (lt_plus_r).
assumption
| rewrite > sym_plus.
rewrite > (sym_times (h11 i j) m1).
|assumption
]
]
-qed.
-
-
-
+qed.
\ No newline at end of file
Morphism_Theory In' Out'.
intros;
apply (mk_Morphism_Theory ? ? f);
- unfold In' in f; clear In';
- unfold Out' in f; clear Out';
+ unfold In' in f ⊢ %; clear In';
+ unfold Out' in f ⊢ %; clear Out';
generalize in match f; clear f;
elim In;
[ unfold make_compatibility_goal;
apply mk_Morphism_Theory;
[ exact Aeq
| unfold make_compatibility_goal;
- simplify;
+ simplify; unfold ASetoidClass; simplify;
intros;
split;
unfold transitive in H;
(Morphism_Theory (cons ? ASetoidClass (singl ? ASetoidClass)) Iff_Relation_Class).
intros;
apply mk_Morphism_Theory;
- reduce;
+ normalize;
[ exact Aeq
| intros;
split;
apply mk_Morphism_Theory;
[ simplify;
apply Aeq
- | simplify;
+ | simplify; unfold ASetoidClass1; simplify; unfold ASetoidClass2; simplify;
intros;
whd;
intros;
apply mk_Morphism_Theory;
[ simplify;
apply Aeq
- | simplify;
+ | simplify; unfold ASetoidClass1; simplify; unfold ASetoidClass2; simplify;
intros;
whd;
intro;
| generalize in match f; clear f;
unfold In'; clear In';
elim In;
- [ reduce;
+ [ normalize;
intro;
apply iff_refl
| simplify;