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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  ⊢  
  : , : , :
1reference30  ⊢  
2instantiation4, 22, 23, 5, 6  ⊢  
  : , : , : , : , :
3instantiation7, 96, 8  ⊢  
  : , : , :
4theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_op_op_is_op
5instantiation21, 22, 23, 9  ⊢  
  : , : , :
6instantiation10, 34, 11  ⊢  
  : , : , :
7axiom  ⊢  
 proveit.physics.quantum.algebra.multi_qmult_def
8instantiation12  ⊢  
  : , :
9instantiation13, 14, 22, 23, 15  ⊢  
  : , : , : , :
10theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_matrix_is_linmap
11instantiation72, 16, 17  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_op_complex_closure
14instantiation38, 18, 19, 20  ⊢  
  : , :
15instantiation21, 22, 23, 24  ⊢  
  : , : , :
16instantiation25, 34  ⊢  
  :
17instantiation26, 74  ⊢  
  :
18instantiation97, 78, 27  ⊢  
  : , : , :
19instantiation28, 71, 29  ⊢  
  : , :
20instantiation30, 31, 32  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_op_is_linmap
22instantiation33, 34  ⊢  
  :
23theorem  ⊢  
 proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
24instantiation35, 74, 36  ⊢  
  : , :
25theorem  ⊢  
 proveit.linear_algebra.matrices.unitaries_are_matrices
26theorem  ⊢  
 proveit.physics.quantum.QFT.invFT_is_unitary
27instantiation97, 86, 37  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
29instantiation38, 61, 71, 48  ⊢  
  : , :
30theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
31instantiation39, 77, 40  ⊢  
  : , :
32instantiation58, 41  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
34instantiation42, 99, 43  ⊢  
  : , :
35theorem  ⊢  
 proveit.physics.quantum.algebra.num_bra_is_lin_map
36assumption  ⊢  
37instantiation97, 92, 44  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.division.div_complex_closure
39theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
40instantiation97, 45, 46  ⊢  
  : , : , :
41instantiation47, 61, 71, 48, 49*  ⊢  
  : , :
42theorem  ⊢  
 proveit.numbers.exponentiation.exp_natpos_closure
43instantiation97, 50, 74  ⊢  
  : , : , :
44instantiation97, 98, 51  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
46instantiation52, 83, 53  ⊢  
  : , :
47theorem  ⊢  
 proveit.numbers.division.div_as_mult
48instantiation54, 96  ⊢  
  :
49instantiation55, 56, 57  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
51theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
52theorem  ⊢  
 proveit.numbers.multiplication.mult_rational_pos_closure_bin
53instantiation97, 95, 74  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
55axiom  ⊢  
 proveit.logic.equality.equals_transitivity
56instantiation58, 59  ⊢  
  : , : , :
57instantiation60, 61, 62  ⊢  
  : , :
58axiom  ⊢  
 proveit.logic.equality.substitution
59instantiation63, 64, 94, 65*  ⊢  
  : , :
60theorem  ⊢  
 proveit.numbers.multiplication.commutation
61instantiation97, 78, 66  ⊢  
  : , : , :
62instantiation97, 78, 67  ⊢  
  : , : , :
63theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
64instantiation97, 68, 69  ⊢  
  : , : , :
65instantiation70, 71  ⊢  
  :
66instantiation72, 73, 74  ⊢  
  : , : , :
67instantiation97, 86, 75  ⊢  
  : , : , :
68theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
69instantiation97, 76, 77  ⊢  
  : , : , :
70theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
71instantiation97, 78, 79  ⊢  
  : , : , :
72theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
73instantiation80, 81  ⊢  
  : , :
74axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
75instantiation97, 82, 83  ⊢  
  : , : , :
76theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
77instantiation97, 84, 85  ⊢  
  : , : , :
78theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
79instantiation97, 86, 87  ⊢  
  : , : , :
80theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
81theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
82theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
83instantiation88, 89, 90  ⊢  
  : , :
84theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
85instantiation97, 91, 96  ⊢  
  : , : , :
86theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
87instantiation97, 92, 93  ⊢  
  : , : , :
88theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
89instantiation97, 95, 94  ⊢  
  : , : , :
90instantiation97, 95, 96  ⊢  
  : , : , :
91theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
92theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
93instantiation97, 98, 99  ⊢  
  : , : , :
94theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
95theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
96theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
97theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
98theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
99theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements