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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,  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
2instantiation4, 5, 6, 7, 8,  ⊢  
  : , : , : , : , :
3instantiation25, 9, 10  ⊢  
  : , : , :
4theorem  ⊢  
 proveit.numbers.division.mult_frac_cancel_denom_left
5instantiation43, 44, 11  ⊢  
  : , : , :
6instantiation43, 44, 12  ⊢  
  : , : , :
7instantiation43, 14, 13  ⊢  
  : , : , :
8instantiation43, 14, 15  ⊢  
  : , : , :
9instantiation34, 16  ⊢  
  : , : , :
10instantiation34, 17  ⊢  
  : , : , :
11instantiation46, 47, 18  ⊢  
  : , : , :
12instantiation43, 19, 20  ⊢  
  : , : , :
13instantiation43, 22, 21  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
15instantiation43, 22, 23  ⊢  
  : , : , :
16instantiation34, 24  ⊢  
  : , : , :
17instantiation25, 26, 27  ⊢  
  : , : , :
18assumption  ⊢  
19theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
20instantiation43, 28, 29  ⊢  
  : , : , :
21instantiation43, 31, 30  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
23instantiation43, 31, 32  ⊢  
  : , : , :
24instantiation33, 42  ⊢  
  :
25axiom  ⊢  
 proveit.logic.equality.equals_transitivity
26instantiation34, 35  ⊢  
  : , : , :
27instantiation36, 42  ⊢  
  :
28theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
29instantiation43, 37, 38  ⊢  
  : , : , :
30instantiation43, 40, 39  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
32instantiation43, 40, 48  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
34axiom  ⊢  
 proveit.logic.equality.substitution
35instantiation41, 42  ⊢  
  :
36theorem  ⊢  
 proveit.numbers.division.frac_one_denom
37theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
38theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
39theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
40theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
41theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
42instantiation43, 44, 45  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
45instantiation46, 47, 48  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
47instantiation49, 50  ⊢  
  : , :
48assumption  ⊢  
49theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
50theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real