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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  ⊢  
  :
1theorem  ⊢  
 proveit.numbers.exponentiation.exp_zero_eq_one
2instantiation3, 4, 5  ⊢  
  : , :
3theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
4instantiation72, 48, 6  ⊢  
  : , : , :
5instantiation7, 8, 9  ⊢  
  : , : , :
6instantiation72, 38, 10  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
8instantiation15, 16, 11  ⊢  
  : , :
9instantiation12, 13, 14  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
11instantiation15, 24, 25  ⊢  
  : , :
12axiom  ⊢  
 proveit.logic.equality.equals_transitivity
13instantiation17, 71, 51, 18, 21, 19, 16, 24, 25  ⊢  
  : , : , : , : , : , :
14instantiation17, 18, 51, 19, 20, 21, 22, 23, 24, 25  ⊢  
  : , : , : , : , : , :
15theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
16instantiation72, 48, 26  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.multiplication.disassociation
18axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
19theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
20instantiation27  ⊢  
  : , :
21instantiation27  ⊢  
  : , :
22instantiation72, 48, 32  ⊢  
  : , : , :
23instantiation72, 48, 33  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
25instantiation28, 29, 30  ⊢  
  : , :
26instantiation31, 32, 33  ⊢  
  : , :
27theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
28theorem  ⊢  
 proveit.numbers.addition.add_complex_closure_bin
29instantiation72, 48, 34  ⊢  
  : , : , :
30instantiation35, 36  ⊢  
  :
31theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
32instantiation72, 52, 37  ⊢  
  : , : , :
33instantiation72, 38, 39  ⊢  
  : , : , :
34instantiation40, 41  ⊢  
  :
35theorem  ⊢  
 proveit.numbers.negation.complex_closure
36instantiation42, 43, 44, 45  ⊢  
  : , :
37instantiation72, 57, 46  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
39theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
40theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
41theorem  ⊢  
 proveit.physics.quantum.QPE._best_floor_is_int
42theorem  ⊢  
 proveit.numbers.division.div_complex_closure
43instantiation72, 48, 47  ⊢  
  : , : , :
44instantiation72, 48, 49  ⊢  
  : , : , :
45instantiation50, 56  ⊢  
  :
46instantiation72, 70, 51  ⊢  
  : , : , :
47instantiation72, 52, 53  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
49instantiation54, 55, 56  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
51theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
52theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
53instantiation72, 57, 58  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
55instantiation59, 60  ⊢  
  : , :
56theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
57theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
58instantiation72, 61, 62  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
60theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
61instantiation63, 64, 69  ⊢  
  : , :
62assumption  ⊢  
63theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
64instantiation65, 66, 67  ⊢  
  : , :
65theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
66instantiation68, 69  ⊢  
  :
67instantiation72, 70, 71  ⊢  
  : , : , :
68theorem  ⊢  
 proveit.numbers.negation.int_closure
69instantiation72, 73, 74  ⊢  
  : , : , :
70theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
71theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
72theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
73theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
74theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos