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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  ⊢  
  : , : , :
1reference11  ⊢  
2instantiation11, 3  ⊢  
  : , : , :
3instantiation4, 5, 6, 7  ⊢  
  : , : , : , :
4theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
5instantiation11, 8  ⊢  
  : , : , :
6instantiation9, 10  ⊢  
  : , :
7instantiation11, 12  ⊢  
  : , : , :
8instantiation13, 14, 15  ⊢  
  : , :
9theorem  ⊢  
 proveit.logic.equality.equals_reversal
10instantiation16, 17, 23, 22, 18  ⊢  
  : , : , :
11axiom  ⊢  
 proveit.logic.equality.substitution
12instantiation19, 20, 21  ⊢  
  : , :
13theorem  ⊢  
 proveit.numbers.addition.commutation
14instantiation49, 24, 22  ⊢  
  : , : , :
15instantiation49, 24, 23  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.exponentiation.product_of_real_powers
17instantiation49, 24, 25  ⊢  
  : , : , :
18instantiation26, 48  ⊢  
  :
19theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
20instantiation49, 27, 28  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
22instantiation29, 30, 31  ⊢  
  : , : , :
23instantiation49, 33, 32  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
25instantiation49, 33, 34  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
27theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
28instantiation49, 35, 36  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
30instantiation37, 38  ⊢  
  : , :
31axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
32instantiation49, 40, 39  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
34instantiation49, 40, 41  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
36instantiation49, 42, 43  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
38theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
39instantiation44, 45  ⊢  
  :
40theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
41instantiation49, 50, 46  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
43instantiation49, 47, 48  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.negation.int_closure
45instantiation49, 50, 51  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
47theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
48theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
49theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
51theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1