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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, 6, 7, 8, 9  ⊢  
  : , : , : , : , : , :
1theorem  ⊢  
 proveit.numbers.multiplication.distribute_through_sum
2reference39  ⊢  
3reference34  ⊢  
4axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
5instantiation10  ⊢  
  : , :
6theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7instantiation11, 12, 13, 14  ⊢  
  : , :
8instantiation37, 17, 15  ⊢  
  : , : , :
9reference13  ⊢  
10theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
11theorem  ⊢  
 proveit.numbers.division.div_complex_closure
12instantiation37, 17, 16  ⊢  
  : , : , :
13instantiation37, 17, 18  ⊢  
  : , : , :
14instantiation19, 20  ⊢  
  :
15instantiation21, 22, 36  ⊢  
  : , : , :
16instantiation37, 24, 23  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
18instantiation37, 24, 25  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
20theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
21theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
22instantiation26, 27  ⊢  
  : , :
23instantiation37, 29, 28  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
25instantiation37, 29, 30  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
27theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
28instantiation31, 32, 33  ⊢  
  : , :
29theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
30instantiation37, 38, 34  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
32instantiation37, 35, 36  ⊢  
  : , : , :
33instantiation37, 38, 39  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
35theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
36assumption  ⊢  
37theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
38theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
39theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1