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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, 18, 23, 19  ⊢  
  : , : , :
11axiom  ⊢  
 proveit.logic.equality.substitution
12instantiation20, 21, 22  ⊢  
  : , :
13theorem  ⊢  
 proveit.numbers.addition.commutation
14instantiation51, 34, 23  ⊢  
  : , : , :
15instantiation24, 25  ⊢  
  :
16theorem  ⊢  
 proveit.numbers.exponentiation.product_of_real_powers
17instantiation51, 34, 26  ⊢  
  : , : , :
18instantiation27, 35  ⊢  
  :
19instantiation28, 50  ⊢  
  :
20theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
21instantiation51, 29, 30  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
23instantiation31, 32, 33  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.negation.complex_closure
25instantiation51, 34, 35  ⊢  
  : , : , :
26instantiation51, 41, 36  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.negation.real_closure
28theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
29theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
30instantiation51, 37, 38  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
32instantiation39, 40  ⊢  
  : , :
33axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
34theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
35instantiation51, 41, 42  ⊢  
  : , : , :
36instantiation51, 46, 43  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
38instantiation51, 44, 45  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
41theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
42instantiation51, 46, 47  ⊢  
  : , : , :
43instantiation51, 52, 48  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
45instantiation51, 49, 50  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
47instantiation51, 52, 53  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
49theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
50theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
51theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
52theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
53theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1