Thm* i: , E:({...i} Prop).
E(i)  ( k:{...i-1}. E(k+1)  E(k))  ( k:{...i}. E(k)) | [int_lower_ind] |
Thm* n: . WellFnd{i}({...n};x,y.x > y) | [int_lower_well_founded] |
Thm* a: , n:{...-1}. (a rem n) = (a rem -n) | [rem_4_to_1] |
Thm* a:{...0}, n:{...-1}. (a rem n) = -((-a) rem -n) | [rem_3_to_1] |
Thm* a:{...0}, n: . (a rem n) = -((-a) rem n) | [rem_2_to_1] |
Thm* a: , b:{...-1}. (a b) = -(a (-b)) | [div_4_to_1] |
Thm* a:{...0}, b:{...-1}. (a b) = ((-a) (-b)) | [div_3_to_1] |
Thm* a:{...0}, b: . (a b) = -((-a) b) | [div_2_to_1] |
Thm* a: , n:{...-1}. 0 (a rem n) & (a rem n) < -n | [rem_bounds_4] |
Thm* a:{...0}, n:{...-1}. 0 (a rem n) & (a rem n) > n | [rem_bounds_3] |
Thm* a:{...0}, n: . 0 (a rem n) & (a rem n) > -n | [rem_bounds_2] |
Thm* i:{...0}. |i| = -i | [absval_neg] |