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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  ⊢  
  : , : , :
1reference24  ⊢  
2reference25  ⊢  
3reference26  ⊢  
4instantiation33, 5, 6  ⊢  
  : , : , :
5instantiation7, 25, 26, 8, 9  ⊢  
  : , : , : , : , :
6instantiation10, 99, 11  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_op_op_is_op
8instantiation24, 25, 26, 12  ⊢  
  : , : , :
9instantiation13, 37, 14  ⊢  
  : , : , :
10axiom  ⊢  
 proveit.physics.quantum.algebra.multi_qmult_def
11instantiation15  ⊢  
  : , :
12instantiation16, 17, 25, 26, 18  ⊢  
  : , : , : , :
13theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_matrix_is_linmap
14instantiation75, 19, 20  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
16theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_op_complex_closure
17instantiation41, 21, 22, 23  ⊢  
  : , :
18instantiation24, 25, 26, 27  ⊢  
  : , : , :
19instantiation28, 37  ⊢  
  :
20instantiation29, 77  ⊢  
  :
21instantiation100, 81, 30  ⊢  
  : , : , :
22instantiation31, 74, 32  ⊢  
  : , :
23instantiation33, 34, 35  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_op_is_linmap
25instantiation36, 37  ⊢  
  :
26theorem  ⊢  
 proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
27instantiation38, 77, 39  ⊢  
  : , :
28theorem  ⊢  
 proveit.linear_algebra.matrices.unitaries_are_matrices
29theorem  ⊢  
 proveit.physics.quantum.QFT.invFT_is_unitary
30instantiation100, 89, 40  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
32instantiation41, 64, 74, 51  ⊢  
  : , :
33theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
34instantiation42, 80, 43  ⊢  
  : , :
35instantiation61, 44  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
37instantiation45, 102, 46  ⊢  
  : , :
38theorem  ⊢  
 proveit.physics.quantum.algebra.num_bra_is_lin_map
39assumption  ⊢  
40instantiation100, 95, 47  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.division.div_complex_closure
42theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
43instantiation100, 48, 49  ⊢  
  : , : , :
44instantiation50, 64, 74, 51, 52*  ⊢  
  : , :
45theorem  ⊢  
 proveit.numbers.exponentiation.exp_natpos_closure
46instantiation100, 53, 77  ⊢  
  : , : , :
47instantiation100, 101, 54  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
49instantiation55, 86, 56  ⊢  
  : , :
50theorem  ⊢  
 proveit.numbers.division.div_as_mult
51instantiation57, 99  ⊢  
  :
52instantiation58, 59, 60  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
54theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
55theorem  ⊢  
 proveit.numbers.multiplication.mult_rational_pos_closure_bin
56instantiation100, 98, 77  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
58axiom  ⊢  
 proveit.logic.equality.equals_transitivity
59instantiation61, 62  ⊢  
  : , : , :
60instantiation63, 64, 65  ⊢  
  : , :
61axiom  ⊢  
 proveit.logic.equality.substitution
62instantiation66, 67, 97, 68*  ⊢  
  : , :
63theorem  ⊢  
 proveit.numbers.multiplication.commutation
64instantiation100, 81, 69  ⊢  
  : , : , :
65instantiation100, 81, 70  ⊢  
  : , : , :
66theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
67instantiation100, 71, 72  ⊢  
  : , : , :
68instantiation73, 74  ⊢  
  :
69instantiation75, 76, 77  ⊢  
  : , : , :
70instantiation100, 89, 78  ⊢  
  : , : , :
71theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
72instantiation100, 79, 80  ⊢  
  : , : , :
73theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
74instantiation100, 81, 82  ⊢  
  : , : , :
75theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
76instantiation83, 84  ⊢  
  : , :
77axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
78instantiation100, 85, 86  ⊢  
  : , : , :
79theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
80instantiation100, 87, 88  ⊢  
  : , : , :
81theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
82instantiation100, 89, 90  ⊢  
  : , : , :
83theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
84theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
85theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
86instantiation91, 92, 93  ⊢  
  : , :
87theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
88instantiation100, 94, 99  ⊢  
  : , : , :
89theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
90instantiation100, 95, 96  ⊢  
  : , : , :
91theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
92instantiation100, 98, 97  ⊢  
  : , : , :
93instantiation100, 98, 99  ⊢  
  : , : , :
94theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
95theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
96instantiation100, 101, 102  ⊢  
  : , : , :
97theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
98theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
99theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
100theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
101theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
102theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements