Thm* i,j: , F:({i..j } Prop).
( k:{i..j }. Dec(F(k)))  Dec( k:{i..j }. F(k)) | [decidable__all_int_seg] |
Thm* i,j: , F:({i..j } Prop).
( k:{i..j }. Dec(F(k)))  Dec( k:{i..j }. F(k)) | [decidable__ex_int_seg] |
Thm* i: , j:{i+1...}, E:({i..j } Prop).
E(i)  ( k:{(i+1)..j }. E(k-1)  E(k))  ( k:{i..j }. E(k)) | [int_seg_ind] |
Thm* i: , E:({...i} Prop).
E(i)  ( k:{...i-1}. E(k+1)  E(k))  ( k:{...i}. E(k)) | [int_lower_ind] |
Thm* i: , E:({i...} Prop).
E(i)  ( k:{i+1...}. E(k-1)  E(k))  ( k:{i...}. E(k)) | [int_upper_ind] |
Thm* P:(  Prop). ( x: . P(|x|))  ( x: . P(x)) | [absval_elim] |