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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  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.addition.add_complex_closure_bin
2instantiation57, 31, 45  ⊢  
  : , : , :
3instantiation4, 5  ⊢  
  :
4theorem  ⊢  
 proveit.numbers.negation.complex_closure
5instantiation6, 7, 8  ⊢  
  : , :
6theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
7instantiation57, 31, 9  ⊢  
  : , : , :
8instantiation10, 11, 12  ⊢  
  : , : , :
9instantiation57, 38, 13  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
11instantiation18, 19, 14  ⊢  
  : , :
12instantiation15, 16, 17  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
14instantiation18, 27, 28  ⊢  
  : , :
15axiom  ⊢  
 proveit.logic.equality.equals_transitivity
16instantiation20, 56, 59, 21, 24, 22, 19, 27, 28  ⊢  
  : , : , : , : , : , :
17instantiation20, 21, 59, 22, 23, 24, 25, 26, 27, 28  ⊢  
  : , : , : , : , : , :
18theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
19instantiation57, 31, 29  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.multiplication.disassociation
21axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
22theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
23instantiation30  ⊢  
  : , :
24instantiation30  ⊢  
  : , :
25instantiation57, 31, 46  ⊢  
  : , : , :
26instantiation57, 31, 34  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
28instantiation57, 31, 32  ⊢  
  : , : , :
29instantiation33, 46, 34  ⊢  
  : , :
30theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
31theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
32instantiation35, 36, 41, 37  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
34instantiation57, 38, 39  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
36instantiation40, 41  ⊢  
  :
37instantiation42, 43  ⊢  
  :
38theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
39theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
40theorem  ⊢  
 proveit.numbers.negation.real_closure
41instantiation44, 45, 46, 47  ⊢  
  : , :
42theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
43assumption  ⊢  
44theorem  ⊢  
 proveit.numbers.division.div_real_closure
45instantiation57, 49, 48  ⊢  
  : , : , :
46instantiation57, 49, 50  ⊢  
  : , : , :
47instantiation51, 52  ⊢  
  :
48instantiation57, 54, 53  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
50instantiation57, 54, 55  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
52theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
53instantiation57, 58, 56  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
55instantiation57, 58, 59  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
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