Proof of filterP_ord_incrF_S.
WIP: sorted_ordP.

WIP: filterP_ord_incrF_S.

Add and prove map_nth_invF.
Proof of perm_EX.

WIP: perm_EX.

Add and prove ltn_asym.

ord_compl:
Add and prove ord_leq_{refl,antisym,trans},
              ord_ltn_{irrefl,asym,trans,total_strict}.

Finite_family:
Propagate new API (from ord_compl).

Add and prove skipF_2{l,r}0, skipF_3{l,m,r}{0,1},
              skipF_coupleF_{l,r}, skipF_tripleF_{l,m,r}.

multi_index:
Propagate new API (from Finite_family).

Some cleaning.
Move stuff around.
Add and prove nat_le_total, nat_lt_total_strict, le_neq_lt, nat_ltS.

ord_compl:
Simplify/compact some proofs.
Move stuff around.
Move is_orderedF stuff from Monoid_compl.
Rename is_orderedF* -> sortedF*,
       is_orderedF_S_aux -> sortedF_S_sortedF_aux,
       is_orderedF_S -> sortedF_S_sortedF.
Add def sortedF_S.
Modify sortedF_inj, sortedF_S_sortedF_aux, sortedF_S_sortedF.
Add and prove sortedF_sortedF_S, sortedF_equiv.
Add defs ord_le, ord_lt, ord_ltn.
Add and prove ord_le_{refl,antisym,trans,total},
              ord_lt_{irrefl,asym,trans,total_strict}.
Modify defs incrF{,_S}.
Proof of incrF_equiv.
Simplify proof of incrF_inj.

Finite_family:
Add defs PAF, PEF, notF, andF, orF, impF, equivF.
Add and prove PF_dec{,_l,_r}.
Simplify proofs of brF_dec{,_l,_r}.
Rename equivF -> equivFA.
Move is_orderedF_castF from Monoid_compl.
Rename is_orderedF_castF -> sortedF_castF,
       skipF_coupleF_{0,1} -> skipF_2{l,r},
       skipF_tripleF_{0,1,2} -> skipF_3{l,m,r}.
Add and prove PAF_ind_{l,r,skipF,skip2F,replaceF,replace2F},
              sortedF_castF_rev, sortedF_castF_equiv.
Rename incrF_Rg_eq_eq_aux -> incrF_Rg_le_0,
       incrF_Rg_eq_eq -> ext_fun_incrF_Rg.
Simplify proofs of Rg_0_liftF_S, incrF_Rg_le_0, ext_fun_incrF_Rg.

Monoid_compl, multi_index:
Propagate new API (from ord_compl, Finite_family).

Monoid_compl:
Move is_orderedF stuff to ord_compl and Finite_family.
Simplify proof of concatnF_order.

multi_index:
Move stuff around.
Rename MO{2,n}_aux{1,2} -> MO{2,n}_correct{1,2}.
Fix MO2_correct{1,2}, MOn_correct2 (commented).
Rename MOn_neq -> MOn_irrefl (modified),
       MOn_total_order -> MOn_total_strict (modified).

Some cleaning (dead code) + some todo.

Simplify proof.

ord_compl:
Add def incrF_S.
WIP: incrF_equiv.

Finite_family:
Proof of injF_restr_bij_EX.

       filterP_f_ord_incrF -> filterP_f_ord_w_incrF.

Add and prove cast_ord_incrF, filterP_cast_ord_incrF.

Finite_family:
WIP: filterP_ord_incrF (modified, use new incrF_Rg_eq_eq).
Modify filterP_f_ord_incrF.

Mv union_inj from Algebra.Finite_family to union_inj_r.
Add union_inj_l, inter_inj_{l,r}.

Finite_family:
Rename widenF_S_inj -> widenF_S_reg,
       liftF_S_inj -> liftF_S_reg,
       eqAF_0_liftF_S -> extF_liftF_S (modified).
Add and prove widenF_S_compat, eqxFn_equiv,
              widenF_S_nextF_compat, widenF_S_nextF_reg, neqxFn_equiv,
              extF_widenF_S,
              liftF_S_compat, eqxF0_equiv,
              liftF_S_nextF_compat, liftF_S_nextF_reg, neqxF0_equiv.
Mv union_inj to Compl.Subset_compl.union_inj_r.

Finite_dim:
Propagate new API (from Finite_family).

Add injS_equiv_seq (WIP).

Add and prove lt_ltn, le_leq.

ord_compl:
WIP: map_injS_uniq.
Add def in_ordS.
Add and prove nth_ord_enum_alt,
              in_ordS_correct_{l{,_alt},r}, val_in_ordS, in_ordS_injS,
              ord_enumS_eq.
Proof of perm_ord_enum_sort.

Finite_family:
Simplify proof.

Add and prove incrF_comp.
WIP: filterP_ord_incrF.

Finite_family:
Add and prove filterP_ord_Rg{_aux{1,2,3},}.

Add and prove nth_ord_enum.

Finite_family:
WIP: injF_restr_bij_EX, filterP_ord_incrF.

Add and prove inj_contra.

nat_compl:
Add and prove ltn_neq, leq_neq_ltn, ltn_leq_neq, ltn_equiv, ltn_S.
Rename ltS_neq_lt -> ltnS_neq_ltn (proof simplified).

ord_compl:
Propagate new API (from nat_compl).
Add and prove ord_leq_{refl,antisym,trans,total}.

Finite_family:
WIP: injF_restr_bij_EX.

Rename seq_* -> *, path_* -> *.
Move stuff around.
Make some arguments explicit.
Add and prove fun_from_I_0_inj, fun_from_I_0_bij.
Move Finite_family.seq_perm_eq_ex -> perm_EX (modified = fixed),
     Finite_family.seq_sort_perm_ex -> sort_perm_EX (modified = fixed),
     def incrF, incrF_inj, ord_leq from Finite_family.
WIP: sort_perm_EX.

Finite_family:
Move def incrF, incrF_inj, ord_leq to ord_compl,
     seq_perm_eq_ex -> ord_compl.perm_EX (modified = fixed),
     seq_sort_perm_ex -> ord_compl.sort_perm_EX (modified = fixed).
WIP: injF_restr_bij_EX.

Don't qualify idents from seq/path.
Add and prove size_ord_enum.
WIP: perm_ord_enum_sort.

Finite_family:
Don't qualify idents from seq/path.
TODWIP: seq_sort_perm_ex (to be fixed).

Add def ord_leq.
Rename path_sort_permut -> seq_sort_perm_ex.
WIP: seq_perm_eq_ex, seq_sort_perm_ex, injF_restr_bij_EX.

Modify def incrF (Nat.lt -> ltn).
Adapt proof of incrF_inj.
WIP: path_sort_permut, injF_restr_bij_EX.

Add and prove inj_equiv.

nat_compl:
Remove double nat_eq_leq (use Nat.le_0_r instead).
Rename nat_eq_leq -> nat_eq_le.

ord_compl:
Rename inj_ord_* -> injF_*.
Add and prove injF_le, surjF_le, lenPF_n0_alt.

Finite_family, Monoid_compl, Finite_dim:
Propagate new API (from nat_compl, ord_compl).

Finite_family:
Add and prove filterP_f_ord_correct_alt.
WIP: filterP_ord_incrF.

Make *explicit* some arguments!

Finite_family:
Add and prove incrF_inj.
Rename injF_restr_bij_EX -> injF_restr_bij_EX' (should be removed).
Add new def injF_restr_bij_EX (simpler).
Add and prove  extendPF_incrF.
WIP: filterP_ord_incrF.
Rename, move and prove filterP_f_ord_incr -> filterP_f_ord_incrF.
Adapt filter*_unfunF* to new def injF_restr_bij_EX.

Monoid_compl, AffineSpace:
Propagate new API (from Finite_family).

Proof of filterPF_unfunF.
WIP: filterP_f_ord_incr.

Add and prove extendPF_permutF.
WIP: filterPF_unfunF (almost there?)

Some cleaning.
add and prove incl_RgF.

Finite_family:
filterPF_unfunF is necessary!
Add def filterP_f_ord.
Add and prove filt erP_f_ord_correct, filterP_f_ord_comp,
Modify filterPF_permutF, filterPF_funF, filterPF_unfunF.
Propagate modifications.
Proof of filterPF_permutF.
WIP: extendPF_refl, filterP_f_ord_comp_l, filterPF_unfunF.

Monoid_compl, AffineSpace:
Propagate new APi (from Finite_family).

Rm useless hypothesis.

Finite_family:
Some cleaning.
TODO: check filterPF_unfunF is really useful.

Add and prove comp_assoc.

Finite_family:
WIP: filterPF_unfunF (modified).
Propagate to filter_neqF_gen_unfunF{,_l}, filter_neqF_unfunF.

Monoid_compl, AffineSpace:
Propagate new APi (from Finite_family).