ExamplesFirst OrderProperties of lists

Properties of Lists

lists.lf
nat : type.
z : nat.
s : nat -> nat.
 
list : type.
nil : list.
cons : {n:nat} {l:list} list.
 
eq_list : {L1:list}{L2:list}type.
refl_list : {L:list} eq_list L L.
 
append : {L1:list}{L2:list}{L3:list} type.
append_nil : {L:list} append nil L L.
append_cons : {L1:list}{L2:list}{L3:list}{N:nat}{D:append L1 L2 L3}
  append (cons N L1) L2 (cons N L3).
 
rev_app : {L1:list}{L2:list}type.
rev_app_nil : rev_app nil nil.
rev_app_cons : {N:nat} {A:list} {B:list} {BN:list} {D:rev_app A B}
  {D2:append B (cons N nil) BN} rev_app (cons N A) BN.
 
rev_acc : {L1:list}{Acc:list}{L2:list}type.
rev_acc_nil : {L:list} rev_acc nil L L.
rev_acc_cons : {L1:list} {L2:list} {L3:list} {N:nat} {D:rev_acc L1 (cons N L2) L3}
  rev_acc (cons N L1) L2 L3.