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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  ⊢  
  :
1reference14  ⊢  
2instantiation66, 26, 4  ⊢  
  : , : , :
3instantiation5, 45, 6, 7, 8  ⊢  
  : , :
4instantiation9, 10, 19  ⊢  
  : , :
5theorem  ⊢  
 proveit.numbers.multiplication.mult_not_eq_zero
6instantiation11  ⊢  
  : , :
7instantiation12, 13, 22  ⊢  
  : , :
8instantiation14, 15, 16  ⊢  
  :
9theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
10instantiation24, 55, 45  ⊢  
  : , :
11theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
12theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_nonzero_closure
13instantiation66, 17, 18  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
15instantiation66, 26, 19  ⊢  
  : , : , :
16instantiation20, 21, 22, 23  ⊢  
  : , :
17theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
18instantiation66, 32, 43  ⊢  
  : , : , :
19instantiation24, 25, 45  ⊢  
  : , :
20theorem  ⊢  
 proveit.numbers.exponentiation.exp_not_eq_zero
21instantiation66, 26, 25  ⊢  
  : , : , :
22instantiation66, 26, 30  ⊢  
  : , : , :
23instantiation27, 28  ⊢  
  :
24theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
25instantiation29, 30, 31  ⊢  
  : , :
26theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
27theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
28instantiation66, 32, 33  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
30instantiation66, 62, 34  ⊢  
  : , : , :
31instantiation35, 60, 55, 44  ⊢  
  : , :
32theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
33instantiation36, 37, 38  ⊢  
  : , :
34instantiation66, 64, 39  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.division.div_real_closure
36theorem  ⊢  
 proveit.numbers.addition.add_real_pos_closure_bin
37instantiation66, 47, 40  ⊢  
  : , : , :
38instantiation41, 42, 43, 44  ⊢  
  : , :
39instantiation66, 67, 45  ⊢  
  : , : , :
40instantiation66, 52, 46  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.division.div_real_pos_closure
42instantiation66, 47, 48  ⊢  
  : , : , :
43instantiation49, 55, 56  ⊢  
  :
44instantiation50, 51  ⊢  
  : , :
45theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
46theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
47theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
48instantiation66, 52, 53  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
50theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
51instantiation54, 59, 55, 56  ⊢  
  : , :
52theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
53theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
54theorem  ⊢  
 proveit.numbers.ordering.less_is_not_eq
55instantiation57, 59, 60, 61  ⊢  
  : , : , :
56instantiation58, 59, 60, 61  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
58theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
59theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
60instantiation66, 62, 63  ⊢  
  : , : , :
61axiom  ⊢  
 proveit.physics.quantum.QPE._eps_in_interval
62theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
63instantiation66, 64, 65  ⊢  
  : , : , :
64theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
65instantiation66, 67, 68  ⊢  
  : , : , :
66theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
67theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
68theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1