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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,  ⊢  
  : , : , :
1reference4  ⊢  
2instantiation4, 5, 6,  ⊢  
  : , : , :
3instantiation7, 8, 9, 10  ⊢  
  : , : , : , :
4theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
5instantiation11, 23, 24, 12, 13,  ⊢  
  : , : , : , : , :
6instantiation29, 14, 15  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
8instantiation38, 16  ⊢  
  : , : , :
9instantiation38, 17  ⊢  
  : , : , :
10instantiation46, 23  ⊢  
  :
11theorem  ⊢  
 proveit.numbers.division.mult_frac_cancel_denom_left
12instantiation52, 19, 18  ⊢  
  : , : , :
13instantiation52, 19, 20  ⊢  
  : , : , :
14instantiation38, 21  ⊢  
  : , : , :
15instantiation38, 22  ⊢  
  : , : , :
16instantiation40, 23  ⊢  
  :
17instantiation40, 24  ⊢  
  :
18instantiation52, 26, 25  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
20instantiation52, 26, 27  ⊢  
  : , : , :
21instantiation38, 28  ⊢  
  : , : , :
22instantiation29, 30, 31  ⊢  
  : , : , :
23instantiation52, 50, 32  ⊢  
  : , : , :
24instantiation52, 50, 33  ⊢  
  : , : , :
25instantiation52, 35, 34  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
27instantiation52, 35, 36  ⊢  
  : , : , :
28instantiation37, 47  ⊢  
  :
29axiom  ⊢  
 proveit.logic.equality.equals_transitivity
30instantiation38, 39  ⊢  
  : , : , :
31instantiation40, 47  ⊢  
  :
32instantiation55, 56, 41  ⊢  
  : , : , :
33instantiation52, 42, 43  ⊢  
  : , : , :
34instantiation52, 45, 44  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
36instantiation52, 45, 57  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
38axiom  ⊢  
 proveit.logic.equality.substitution
39instantiation46, 47  ⊢  
  :
40theorem  ⊢  
 proveit.numbers.division.frac_one_denom
41assumption  ⊢  
42theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
43instantiation52, 48, 49  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
45theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
46theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
47instantiation52, 50, 51  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
49instantiation52, 53, 54  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
51instantiation55, 56, 57  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
53theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
54theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
55theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
56instantiation58, 59  ⊢  
  : , :
57assumption  ⊢  
58theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
59theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real