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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, 4  ⊢  
  : , : , : , :
1theorem  ⊢  
 proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
2instantiation5, 6  ⊢  
  :
3instantiation7, 8, 9  ⊢  
  : , :
4instantiation10, 67, 53  ⊢  
  : , :
5theorem  ⊢  
 proveit.linear_algebra.complex_vec_set_is_vec_space
6instantiation11, 65, 62  ⊢  
  : , :
7theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
8instantiation68, 43, 12  ⊢  
  : , : , :
9instantiation20, 13, 14  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.physics.quantum.algebra.num_ket_in_register_space
11theorem  ⊢  
 proveit.numbers.exponentiation.exp_natpos_closure
12instantiation68, 48, 15  ⊢  
  : , : , :
13instantiation36, 23, 16  ⊢  
  : , :
14instantiation17, 18, 19  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
16instantiation20, 21, 22  ⊢  
  : , : , :
17axiom  ⊢  
 proveit.logic.equality.equals_transitivity
18instantiation28, 70, 24, 29, 26, 30, 23, 37, 38, 32  ⊢  
  : , : , : , : , : , :
19instantiation28, 29, 65, 24, 30, 25, 26, 33, 34, 37, 38, 32  ⊢  
  : , : , : , : , : , :
20theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
21instantiation36, 27, 32  ⊢  
  : , :
22instantiation28, 29, 65, 70, 30, 31, 37, 38, 32  ⊢  
  : , : , : , : , : , :
23instantiation36, 33, 34  ⊢  
  : , :
24theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
25instantiation39  ⊢  
  : , :
26instantiation35  ⊢  
  : , : , :
27instantiation36, 37, 38  ⊢  
  : , :
28theorem  ⊢  
 proveit.numbers.multiplication.disassociation
29axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
30theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
31instantiation39  ⊢  
  : , :
32instantiation68, 43, 40  ⊢  
  : , : , :
33instantiation68, 43, 41  ⊢  
  : , : , :
34instantiation68, 43, 42  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
36theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
37theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
38instantiation68, 43, 44  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
40instantiation68, 46, 45  ⊢  
  : , : , :
41instantiation68, 46, 47  ⊢  
  : , : , :
42instantiation68, 48, 49  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
44theorem  ⊢  
 proveit.physics.quantum.QPE._phase_is_real
45instantiation68, 51, 50  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
47instantiation68, 51, 61  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
49theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
50instantiation68, 52, 53  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
52instantiation54, 55, 56  ⊢  
  : , :
53assumption  ⊢  
54theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
55theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
56instantiation57, 58, 59  ⊢  
  : , :
57theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
58instantiation60, 61, 62  ⊢  
  : , :
59instantiation63, 64  ⊢  
  :
60theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
61instantiation68, 69, 65  ⊢  
  : , : , :
62instantiation68, 66, 67  ⊢  
  : , : , :
63theorem  ⊢  
 proveit.numbers.negation.int_closure
64instantiation68, 69, 70  ⊢  
  : , : , :
65theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
66theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
67axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
68theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
69theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
70theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1