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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
2instantiation15, 4  ⊢  
  : , : , :
3instantiation15, 5  ⊢  
  : , : , :
4instantiation15, 7  ⊢  
  : , : , :
5instantiation15, 6  ⊢  
  : , : , :
6instantiation15, 7  ⊢  
  : , : , :
7instantiation8, 9, 10, 11  ⊢  
  : , : , : , :
8theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
9instantiation15, 12  ⊢  
  : , : , :
10instantiation13, 14  ⊢  
  : , :
11instantiation15, 16  ⊢  
  : , : , :
12instantiation17, 18, 19  ⊢  
  : , :
13theorem  ⊢  
 proveit.logic.equality.equals_reversal
14instantiation20, 21, 22, 27, 23  ⊢  
  : , : , :
15axiom  ⊢  
 proveit.logic.equality.substitution
16instantiation24, 25, 26  ⊢  
  : , :
17theorem  ⊢  
 proveit.numbers.addition.commutation
18instantiation55, 38, 27  ⊢  
  : , : , :
19instantiation28, 29  ⊢  
  :
20theorem  ⊢  
 proveit.numbers.exponentiation.product_of_real_powers
21instantiation55, 38, 30  ⊢  
  : , : , :
22instantiation31, 39  ⊢  
  :
23instantiation32, 54  ⊢  
  :
24theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
25instantiation55, 33, 34  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
27instantiation35, 36, 37  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.negation.complex_closure
29instantiation55, 38, 39  ⊢  
  : , : , :
30instantiation55, 45, 40  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.negation.real_closure
32theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
33theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
34instantiation55, 41, 42  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
36instantiation43, 44  ⊢  
  : , :
37axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
38theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
39instantiation55, 45, 46  ⊢  
  : , : , :
40instantiation55, 50, 47  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
42instantiation55, 48, 49  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
44theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
45theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
46instantiation55, 50, 51  ⊢  
  : , : , :
47instantiation55, 56, 52  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
49instantiation55, 53, 54  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
51instantiation55, 56, 57  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
53theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
54theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
55theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
56theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
57theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1