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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, ,  ⊢  
  : , : , :
1reference38  ⊢  
2instantiation5, 3, 4, ,  ⊢  
  : , : , :
3instantiation5, 6, 7, ,  ⊢  
  : , : , :
4instantiation8, 9, 10, 11  ⊢  
  : , : , : , :
5theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
6instantiation12, 25, 26, 13, 14, ,  ⊢  
  : , : , : , : , :
7instantiation30, 15, 16  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
9instantiation38, 17  ⊢  
  : , : , :
10instantiation38, 18  ⊢  
  : , : , :
11instantiation45, 25  ⊢  
  :
12theorem  ⊢  
 proveit.numbers.division.mult_frac_cancel_denom_left
13instantiation51, 19, 20  ⊢  
  : , : , :
14instantiation21, 46, 22,  ⊢  
  :
15instantiation38, 23  ⊢  
  : , : , :
16instantiation38, 24  ⊢  
  : , : , :
17instantiation40, 25  ⊢  
  :
18instantiation40, 26  ⊢  
  :
19theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
20instantiation51, 27, 28  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
22assumption  ⊢  
23instantiation38, 29  ⊢  
  : , : , :
24instantiation30, 31, 32  ⊢  
  : , : , :
25instantiation51, 49, 33  ⊢  
  : , : , :
26instantiation51, 49, 34  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
28instantiation51, 35, 36  ⊢  
  : , : , :
29instantiation37, 46  ⊢  
  :
30axiom  ⊢  
 proveit.logic.equality.equals_transitivity
31instantiation38, 39  ⊢  
  : , : , :
32instantiation40, 46  ⊢  
  :
33assumption  ⊢  
34instantiation51, 41, 42  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
36instantiation51, 43, 44  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
38axiom  ⊢  
 proveit.logic.equality.substitution
39instantiation45, 46  ⊢  
  :
40theorem  ⊢  
 proveit.numbers.division.frac_one_denom
41theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
42instantiation51, 47, 48  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
44theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
45theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
46instantiation51, 49, 50  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
48instantiation51, 52, 53  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
50assumption  ⊢  
51theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
52theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
53theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1