logo

Show the Proof

In [1]:
import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof
Out[1]:
 step typerequirementsstatement
0instantiation1, 2, 3,  ⊢  
  : , : , :
1reference17  ⊢  
2instantiation20, 4  ⊢  
  : , : , :
3instantiation5, 6, 7,  ⊢  
  :
4instantiation20, 8  ⊢  
  : , : , :
5theorem  ⊢  
 proveit.numbers.division.frac_cancel_complete
6instantiation9, 25, 10  ⊢  
  : , :
7instantiation11, 12  ⊢  
  : , :
8instantiation20, 13  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.addition.add_complex_closure_bin
10instantiation14, 23  ⊢  
  :
11theorem  ⊢  
 proveit.numbers.addition.subtraction.nonzero_difference_if_different
12instantiation15, 16  ⊢  
  : , :
13instantiation17, 18, 19  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.negation.complex_closure
15theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
16assumption  ⊢  
17axiom  ⊢  
 proveit.logic.equality.equals_transitivity
18instantiation20, 21  ⊢  
  : , : , :
19instantiation22, 23  ⊢  
  :
20axiom  ⊢  
 proveit.logic.equality.substitution
21instantiation24, 25  ⊢  
  :
22theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
23assumption  ⊢  
24theorem  ⊢  
 proveit.numbers.addition.elim_zero_left
25instantiation32, 26, 27  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
27instantiation32, 28, 29  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
29instantiation32, 30, 31  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
31instantiation32, 33, 34  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
33theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
34theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1