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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, 10, , ,  ⊢  
  : , : , : , : , : , : , :
1theorem  ⊢  
 proveit.numbers.multiplication.leftward_commutation
2reference42  ⊢  
3theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
4instantiation11  ⊢  
  : , : , :
5instantiation40, 26, 12  ⊢  
  : , : , :
6instantiation13, 14  ⊢  
  :
7reference18  ⊢  
8instantiation15, 16, 18  ⊢  
  : , :
9instantiation17, 18, 19, 20  ⊢  
  : , :
10instantiation40, 26, 21  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
12instantiation40, 31, 22  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.exponentiation.sqrt_complex_closure
14instantiation40, 26, 23  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
16instantiation40, 26, 24  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.division.div_complex_closure
18instantiation40, 26, 25  ⊢  
  : , : , :
19instantiation40, 26, 27  ⊢  
  : , : , :
20instantiation28, 29  ⊢  
  :
21assumption  ⊢  
22assumption  ⊢  
23instantiation40, 31, 30  ⊢  
  : , : , :
24instantiation40, 31, 32  ⊢  
  : , : , :
25instantiation40, 34, 33  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
27instantiation40, 34, 35  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
29theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat3
30assumption  ⊢  
31theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_neg_within_real
32assumption  ⊢  
33instantiation40, 37, 36  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
35instantiation40, 37, 38  ⊢  
  : , : , :
36instantiation40, 41, 39  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
38instantiation40, 41, 42  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
40theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
41theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
42theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3