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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, 5, 6, 7, , , , , , , ,  ⊢  
  : , : , : , : , :
1theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_pulling_scalar_out_front
2theorem  ⊢  
 proveit.numbers.numerals.decimals.nat7
3axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
4assumption  ⊢  
5instantiation8  ⊢  
  : , : , : , : , : , : , :
6theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7instantiation43, 9, 10, , , , , , ,  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_7_typical_eq
9instantiation11, 12, 13, , , , , , ,  ⊢  
  : , :
10instantiation50, 14, 15  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_complex_left_closure
12instantiation43, 16, 17, , , , , , ,  ⊢  
  : , : , :
13instantiation18, 64, 65,  ⊢  
  : , :
14theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat6
15instantiation19  ⊢  
  : , : , : , : , : , :
16instantiation20, 21, 61, 22, , , , , , ,  ⊢  
  : , : , :
17instantiation50, 23, 24  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_bra_in_QmultCodomain
19theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_6_typical_eq
20theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_complex_ket_closure
21instantiation43, 25, 26, , , , , ,  ⊢  
  : , : , :
22assumption  ⊢  
23theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat5
24instantiation27  ⊢  
  : , : , : , : , :
25instantiation28, 47, 61, 29, 30, , , , , ,  ⊢  
  : , : , : , :
26instantiation50, 31, 32  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
28theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_op_ket_is_ket
29instantiation53, 47, 61, 33, , , , ,  ⊢  
  : , : , :
30assumption  ⊢  
31theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat4
32instantiation34  ⊢  
  : , : , : , :
33instantiation43, 35, 36, , , , ,  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
35instantiation59, 37, 47, 61, 38, , , , ,  ⊢  
  : , : , : , :
36instantiation50, 39, 40  ⊢  
  : , : , :
37assumption  ⊢  
38instantiation53, 47, 61, 41, , , ,  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat3
40instantiation42  ⊢  
  : , : , :
41instantiation43, 44, 45, , , ,  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
43theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
44instantiation46, 47, 64, 61, 48, 49, , , ,  ⊢  
  : , : , : , : , :
45instantiation50, 51, 52  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_op_op_is_op
47instantiation66, 56  ⊢  
  :
48instantiation53, 64, 61, 54, ,  ⊢  
  : , : , :
49instantiation55, 67, 56, 57, ,  ⊢  
  : , : , :
50axiom  ⊢  
 proveit.physics.quantum.algebra.multi_qmult_def
51theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
52instantiation58  ⊢  
  : , :
53theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_op_is_linmap
54instantiation59, 60, 64, 61, 62, ,  ⊢  
  : , : , : , :
55theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_matrix_is_linmap
56assumption  ⊢  
57assumption  ⊢  
58theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
59theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_op_complex_closure
60assumption  ⊢  
61theorem  ⊢  
 proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
62instantiation63, 64, 65,  ⊢  
  : , :
63theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_bra_is_linmap
64instantiation66, 67  ⊢  
  :
65assumption  ⊢  
66theorem  ⊢  
 proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
67assumption  ⊢