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In [1]:
import proveit
theory = proveit.Theory() # the theorem's theory
from proveit import defaults, a, x, y
from proveit.logic import Equals, InSet
from proveit.numbers import Add, Neg, subtract, Real, zero
from proveit.numbers.rounding import Floor
from proveit.numbers.rounding import floor_of_x_less_eq_x
In [2]:
%proving real_minus_floor_lower_bound
With these allowed/disallowed theorem/theory presumptions (e.g., to avoid circular dependencies), we begin our proof of
real_minus_floor_lower_bound:
(see dependencies)
real_minus_floor_lower_bound may now be readily provable (assuming required theorems are usable).  Simply execute "%qed".
In [3]:
%qed
proveit.numbers.rounding.real_minus_floor_lower_bound has been proven.
Out[3]:
 step typerequirementsstatement
0generalization1  ⊢  
1instantiation2, 3  ⊢  
  : , :
2conjecture  ⊢  
 proveit.numbers.addition.subtraction.nonneg_difference
3instantiation4, 5  ⊢  
  :
4axiom  ⊢  
 proveit.numbers.rounding.floor_of_x_less_eq_x
5assumption  ⊢