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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
0generalization1  ⊢  
1instantiation2, 3, 4, 5  ⊢  
  : , : , : , :
2theorem  ⊢  
 proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
3instantiation6, 7  ⊢  
  :
4instantiation8, 9, 10  ⊢  
  : , :
5instantiation11, 68, 54  ⊢  
  : , :
6theorem  ⊢  
 proveit.linear_algebra.complex_vec_set_is_vec_space
7instantiation12, 66, 63  ⊢  
  : , :
8theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
9instantiation69, 44, 13  ⊢  
  : , : , :
10instantiation21, 14, 15  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.physics.quantum.algebra.num_ket_in_register_space
12theorem  ⊢  
 proveit.numbers.exponentiation.exp_natpos_closure
13instantiation69, 49, 16  ⊢  
  : , : , :
14instantiation37, 24, 17  ⊢  
  : , :
15instantiation18, 19, 20  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
17instantiation21, 22, 23  ⊢  
  : , : , :
18axiom  ⊢  
 proveit.logic.equality.equals_transitivity
19instantiation29, 71, 25, 30, 27, 31, 24, 38, 39, 33  ⊢  
  : , : , : , : , : , :
20instantiation29, 30, 66, 25, 31, 26, 27, 34, 35, 38, 39, 33  ⊢  
  : , : , : , : , : , :
21theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
22instantiation37, 28, 33  ⊢  
  : , :
23instantiation29, 30, 66, 71, 31, 32, 38, 39, 33  ⊢  
  : , : , : , : , : , :
24instantiation37, 34, 35  ⊢  
  : , :
25theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
26instantiation40  ⊢  
  : , :
27instantiation36  ⊢  
  : , : , :
28instantiation37, 38, 39  ⊢  
  : , :
29theorem  ⊢  
 proveit.numbers.multiplication.disassociation
30axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
31theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
32instantiation40  ⊢  
  : , :
33instantiation69, 44, 41  ⊢  
  : , : , :
34instantiation69, 44, 42  ⊢  
  : , : , :
35instantiation69, 44, 43  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
37theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
38theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
39instantiation69, 44, 45  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
41instantiation69, 47, 46  ⊢  
  : , : , :
42instantiation69, 47, 48  ⊢  
  : , : , :
43instantiation69, 49, 50  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
45theorem  ⊢  
 proveit.physics.quantum.QPE._phase_is_real
46instantiation69, 52, 51  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
48instantiation69, 52, 62  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
50theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
51instantiation69, 53, 54  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
53instantiation55, 56, 57  ⊢  
  : , :
54assumption  ⊢  
55theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
56theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
57instantiation58, 59, 60  ⊢  
  : , :
58theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
59instantiation61, 62, 63  ⊢  
  : , :
60instantiation64, 65  ⊢  
  :
61theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
62instantiation69, 70, 66  ⊢  
  : , : , :
63instantiation69, 67, 68  ⊢  
  : , : , :
64theorem  ⊢  
 proveit.numbers.negation.int_closure
65instantiation69, 70, 71  ⊢  
  : , : , :
66theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
67theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
68axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
69theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
70theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
71theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1