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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*  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_right
2reference9  ⊢  
3reference10  ⊢  
4instantiation5, 6, 7  ⊢  
  : , : , :
5axiom  ⊢  
 proveit.logic.equality.equals_transitivity
6instantiation8, 9, 10  ⊢  
  : , :
7instantiation11, 22, 12, 13, 14*, 15*  ⊢  
  : , : , : , :
8theorem  ⊢  
 proveit.numbers.multiplication.commutation
9instantiation57, 44, 16  ⊢  
  : , : , :
10instantiation57, 44, 17  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.division.prod_of_fracs
12instantiation57, 19, 18  ⊢  
  : , : , :
13instantiation57, 19, 20  ⊢  
  : , : , :
14instantiation21, 22  ⊢  
  :
15instantiation23, 36, 24, 25, 26*  ⊢  
  : , : , :
16instantiation29, 34, 27, 28  ⊢  
  : , :
17instantiation29, 34, 45, 30  ⊢  
  : , :
18instantiation57, 32, 31  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
20instantiation57, 32, 33  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
22instantiation57, 44, 34  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.exponentiation.product_of_posnat_powers
24theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
25axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
26instantiation35, 36  ⊢  
  :
27instantiation37, 38, 50  ⊢  
  : , : , :
28instantiation39, 50  ⊢  
  :
29theorem  ⊢  
 proveit.numbers.division.div_real_closure
30instantiation39, 48  ⊢  
  :
31instantiation57, 41, 40  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
33instantiation57, 41, 42  ⊢  
  : , : , :
34instantiation57, 52, 43  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
36instantiation57, 44, 45  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
38instantiation46, 47  ⊢  
  : , :
39theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
40instantiation57, 49, 48  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
42instantiation57, 49, 50  ⊢  
  : , : , :
43instantiation57, 55, 51  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
45instantiation57, 52, 53  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
47theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
48theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
49theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
50theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
51instantiation57, 58, 54  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
53instantiation57, 55, 56  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
55theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
56instantiation57, 58, 59  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
59theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements