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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, 4, 5  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.numbers.addition.subtraction.subtract_from_add
2instantiation57, 51, 6  ⊢  
  : , : , :
3instantiation57, 51, 7  ⊢  
  : , : , :
4instantiation57, 51, 8  ⊢  
  : , : , :
5theorem  ⊢  
 proveit.numbers.numerals.decimals.add_9_3
6instantiation57, 53, 9  ⊢  
  : , : , :
7instantiation57, 53, 10  ⊢  
  : , : , :
8instantiation57, 53, 11  ⊢  
  : , : , :
9instantiation57, 55, 12  ⊢  
  : , : , :
10instantiation57, 55, 13  ⊢  
  : , : , :
11instantiation57, 55, 14  ⊢  
  : , : , :
12instantiation57, 58, 15  ⊢  
  : , : , :
13instantiation57, 58, 16  ⊢  
  : , : , :
14instantiation57, 17, 18  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.numerals.decimals.nat9
16theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
17theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
18instantiation19, 31, 20, 21, 22  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.numerals.decimals.deci_sequence_is_nat_pos
20instantiation24, 31, 23  ⊢  
  :
21instantiation24, 59, 25  ⊢  
  :
22theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
23instantiation28, 26, 27  ⊢  
  : , :
24theorem  ⊢  
 proveit.numbers.numerals.decimals.n_in_digits
25instantiation28, 29, 30  ⊢  
  : , :
26instantiation41, 31  ⊢  
  :
27instantiation32, 33  ⊢  
  :
28theorem  ⊢  
 proveit.logic.booleans.conjunction.and_if_both
29instantiation41, 59  ⊢  
  :
30instantiation34, 52, 35, 36, 37, 38*, 39*  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
32theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
33theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat9
34theorem  ⊢  
 proveit.numbers.addition.weak_bound_via_left_term_bound
35theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
36instantiation57, 53, 40  ⊢  
  : , : , :
37instantiation41, 50  ⊢  
  :
38instantiation42, 43, 44  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.numerals.decimals.add_7_2
40instantiation57, 55, 45  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_lower_bound
42theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
43instantiation46, 48  ⊢  
  :
44instantiation47, 48, 49  ⊢  
  : , :
45instantiation57, 58, 50  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.addition.elim_zero_right
47theorem  ⊢  
 proveit.numbers.addition.commutation
48instantiation57, 51, 52  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
50theorem  ⊢  
 proveit.numbers.numerals.decimals.nat7
51theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
52instantiation57, 53, 54  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
54instantiation57, 55, 56  ⊢  
  : , : , :
55theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
56instantiation57, 58, 59  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
59theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements