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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.numbers.number_sets.integers.nonneg_int_is_natural
2instantiation35, 4, 5  ⊢  
  : , :
3instantiation6, 7  ⊢  
  : , :
4instantiation66, 67, 8  ⊢  
  : , : , :
5instantiation62, 26  ⊢  
  :
6theorem  ⊢  
 proveit.numbers.addition.subtraction.nonneg_difference
7instantiation9, 10, 11, 48, 12, 13*, 14*  ⊢  
  : , : , :
8instantiation15, 16  ⊢  
  : , :
9theorem  ⊢  
 proveit.numbers.addition.weak_bound_via_left_term_bound
10instantiation66, 55, 17  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
12instantiation18, 19  ⊢  
  : , :
13instantiation30, 20, 21  ⊢  
  : , : , :
14instantiation22, 23, 24, 25  ⊢  
  : , : , : , :
15theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
16theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
17instantiation66, 60, 26  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.ordering.relax_less
19instantiation27, 68  ⊢  
  :
20instantiation36, 37, 65, 38, 39, 40, 28, 41, 44  ⊢  
  : , : , : , : , : , :
21instantiation29, 38, 65, 40, 39, 41, 44  ⊢  
  : , : , : , :
22theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
23instantiation30, 31, 32  ⊢  
  : , : , :
24instantiation51  ⊢  
  :
25instantiation33, 34  ⊢  
  : , :
26instantiation35, 57, 61  ⊢  
  : , :
27theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
28theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
29theorem  ⊢  
 proveit.numbers.addition.elim_zero_any
30axiom  ⊢  
 proveit.logic.equality.equals_transitivity
31instantiation36, 37, 65, 38, 39, 40, 43, 41, 44  ⊢  
  : , : , : , : , : , :
32instantiation42, 43, 44, 45  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.logic.equality.equals_reversal
34theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
35theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
36theorem  ⊢  
 proveit.numbers.addition.disassociation
37theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
38axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
39instantiation46  ⊢  
  : , :
40theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
41instantiation66, 49, 47  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_12
43instantiation66, 49, 48  ⊢  
  : , : , :
44instantiation66, 49, 50  ⊢  
  : , : , :
45instantiation51  ⊢  
  :
46theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
47instantiation66, 55, 52  ⊢  
  : , : , :
48instantiation53, 54, 68  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
50instantiation66, 55, 56  ⊢  
  : , : , :
51axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
52instantiation66, 60, 57  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
54instantiation58, 59  ⊢  
  : , :
55theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
56instantiation66, 60, 61  ⊢  
  : , : , :
57instantiation62, 63  ⊢  
  :
58theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
59theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
60theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
61instantiation66, 64, 65  ⊢  
  : , : , :
62theorem  ⊢  
 proveit.numbers.negation.int_closure
63instantiation66, 67, 68  ⊢  
  : , : , :
64theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
65theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
66theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
67theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
68assumption  ⊢  
*equality replacement requirements