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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, 22, 12, 13  ⊢  
  : , : , : , : , :
6instantiation28, 14, 15  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
8instantiation37, 16  ⊢  
  : , : , :
9instantiation37, 16  ⊢  
  : , : , :
10instantiation45, 22  ⊢  
  :
11theorem  ⊢  
 proveit.numbers.division.mult_frac_cancel_denom_left
12instantiation59, 18, 17  ⊢  
  : , : , :
13instantiation59, 18, 19  ⊢  
  : , : , :
14instantiation37, 20  ⊢  
  : , : , :
15instantiation37, 21  ⊢  
  : , : , :
16instantiation39, 22  ⊢  
  :
17instantiation59, 23, 24  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
19instantiation59, 25, 26  ⊢  
  : , : , :
20instantiation37, 27  ⊢  
  : , : , :
21instantiation28, 29, 30  ⊢  
  : , : , :
22instantiation59, 53, 31  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
24instantiation59, 32, 33  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
26instantiation34, 35  ⊢  
  :
27instantiation36, 46  ⊢  
  :
28axiom  ⊢  
 proveit.logic.equality.equals_transitivity
29instantiation37, 38  ⊢  
  : , : , :
30instantiation39, 46  ⊢  
  :
31instantiation59, 55, 40  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
33instantiation59, 41, 42  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.exponentiation.sqrt_real_pos_closure
35instantiation59, 43, 44  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
37axiom  ⊢  
 proveit.logic.equality.substitution
38instantiation45, 46  ⊢  
  :
39theorem  ⊢  
 proveit.numbers.division.frac_one_denom
40instantiation59, 57, 47  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
42theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
43theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
44instantiation59, 48, 49  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
46instantiation50, 51  ⊢  
  :
47instantiation59, 60, 52  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
49theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
50theorem  ⊢  
 proveit.numbers.exponentiation.sqrt_complex_closure
51instantiation59, 53, 54  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
53theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
54instantiation59, 55, 56  ⊢  
  : , : , :
55theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
56instantiation59, 57, 58  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
58instantiation59, 60, 61  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
60theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
61theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2