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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.negation.complex_closure
2instantiation3, 4, 5  ⊢  
  : , :
3theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
4instantiation55, 40, 6  ⊢  
  : , : , :
5instantiation14, 7, 8  ⊢  
  : , : , :
6instantiation55, 47, 9  ⊢  
  : , : , :
7instantiation32, 17, 10  ⊢  
  : , :
8instantiation11, 12, 13  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
10instantiation14, 15, 16  ⊢  
  : , : , :
11axiom  ⊢  
 proveit.logic.equality.equals_transitivity
12instantiation24, 26, 18, 25, 20, 27, 17, 33, 34, 29  ⊢  
  : , : , : , : , : , :
13instantiation24, 25, 57, 18, 27, 19, 20, 21, 22, 33, 34, 29  ⊢  
  : , : , : , : , : , :
14theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
15instantiation32, 23, 29  ⊢  
  : , :
16instantiation24, 25, 57, 26, 27, 28, 33, 34, 29  ⊢  
  : , : , : , : , : , :
17instantiation55, 40, 30  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
19instantiation35  ⊢  
  : , :
20instantiation31  ⊢  
  : , : , :
21instantiation55, 40, 38  ⊢  
  : , : , :
22instantiation55, 40, 39  ⊢  
  : , : , :
23instantiation32, 33, 34  ⊢  
  : , :
24theorem  ⊢  
 proveit.numbers.multiplication.disassociation
25axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
26theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
27theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
28instantiation35  ⊢  
  : , :
29instantiation55, 40, 36  ⊢  
  : , : , :
30instantiation37, 38, 39  ⊢  
  : , :
31theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
32theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
33theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
34instantiation55, 40, 41  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
36instantiation42, 43, 44  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
38instantiation55, 45, 46  ⊢  
  : , : , :
39instantiation55, 47, 48  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
41instantiation49, 50  ⊢  
  :
42theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
43instantiation51, 52  ⊢  
  : , :
44theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
45theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
46instantiation55, 53, 54  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
48theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
49theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
50theorem  ⊢  
 proveit.physics.quantum.QPE._best_round_is_int
51theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
52theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
53theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
54instantiation55, 56, 57  ⊢  
  : , : , :
55theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
56theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
57theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2