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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  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.equals_transitivity
2instantiation5, 6, 38, 46, 9, 7, 10, 11, 4  ⊢  
  : , : , : , : , : , :
3instantiation5, 38, 6, 7, 8, 9, 10, 11, 12, 13  ⊢  
  : , : , : , : , : , :
4instantiation44, 26, 14  ⊢  
  : , : , :
5theorem  ⊢  
 proveit.numbers.addition.disassociation
6axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
7instantiation15  ⊢  
  : , :
8instantiation15  ⊢  
  : , :
9theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
10instantiation44, 26, 16  ⊢  
  : , : , :
11instantiation44, 26, 17  ⊢  
  : , : , :
12instantiation44, 26, 18  ⊢  
  : , : , :
13instantiation19, 20  ⊢  
  :
14instantiation44, 33, 21  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
16instantiation44, 33, 22  ⊢  
  : , : , :
17instantiation44, 33, 23  ⊢  
  : , : , :
18instantiation24, 25, 43  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.negation.complex_closure
20instantiation44, 26, 27  ⊢  
  : , : , :
21instantiation44, 39, 28  ⊢  
  : , : , :
22instantiation44, 39, 29  ⊢  
  : , : , :
23instantiation44, 39, 30  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
25instantiation31, 32  ⊢  
  : , :
26theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
27instantiation44, 33, 34  ⊢  
  : , : , :
28instantiation35, 37, 36  ⊢  
  : , :
29instantiation40, 37  ⊢  
  :
30instantiation44, 45, 38  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
32theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
33theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
34instantiation44, 39, 41  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
36instantiation40, 41  ⊢  
  :
37instantiation44, 42, 43  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
39theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
40theorem  ⊢  
 proveit.numbers.negation.int_closure
41instantiation44, 45, 46  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
43assumption  ⊢  
44theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
45theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
46theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1