| Rank | Theorem | Name | 
| 2 |  p,q,r,s:  . p =q q   r =q s   p +q r =q q +q s | [qadd_functionality] | 
| cites the following: | ||
| 1 |  x,y:  . x=  y   x = y | [assert_of_eq_int_rw] | 
| 0 |  a,b,n:  . a = b   n  a = n  b | [mul_preserves_eq] | 
| 0 |  i1,i2,j1,j2:  . i1 = j1   i2 = j2   i1+i2 = j1+j2 | [add_functionality_wrt_eq] |