logo

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, 5  ⊢  
  : , : , : , : , :
1theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_op_op_is_op
2reference18  ⊢  
3reference19  ⊢  
4instantiation17, 18, 19, 6  ⊢  
  : , : , :
5instantiation7, 30, 8  ⊢  
  : , : , :
6instantiation9, 10, 18, 19, 11  ⊢  
  : , : , : , :
7theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_matrix_is_linmap
8instantiation68, 12, 13  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_op_complex_closure
10instantiation34, 14, 15, 16  ⊢  
  : , :
11instantiation17, 18, 19, 20  ⊢  
  : , : , :
12instantiation21, 30  ⊢  
  :
13instantiation22, 70  ⊢  
  :
14instantiation93, 74, 23  ⊢  
  : , : , :
15instantiation24, 67, 25  ⊢  
  : , :
16instantiation26, 27, 28  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.physics.quantum.algebra.qmult_op_is_linmap
18instantiation29, 30  ⊢  
  :
19theorem  ⊢  
 proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
20instantiation31, 70, 32  ⊢  
  : , :
21theorem  ⊢  
 proveit.linear_algebra.matrices.unitaries_are_matrices
22theorem  ⊢  
 proveit.physics.quantum.QFT.invFT_is_unitary
23instantiation93, 82, 33  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
25instantiation34, 57, 67, 44  ⊢  
  : , :
26theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
27instantiation35, 73, 36  ⊢  
  : , :
28instantiation54, 37  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
30instantiation38, 95, 39  ⊢  
  : , :
31theorem  ⊢  
 proveit.physics.quantum.algebra.num_bra_is_lin_map
32assumption  ⊢  
33instantiation93, 88, 40  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.division.div_complex_closure
35theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
36instantiation93, 41, 42  ⊢  
  : , : , :
37instantiation43, 57, 67, 44, 45*  ⊢  
  : , :
38theorem  ⊢  
 proveit.numbers.exponentiation.exp_natpos_closure
39instantiation93, 46, 70  ⊢  
  : , : , :
40instantiation93, 94, 47  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
42instantiation48, 79, 49  ⊢  
  : , :
43theorem  ⊢  
 proveit.numbers.division.div_as_mult
44instantiation50, 92  ⊢  
  :
45instantiation51, 52, 53  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
47theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
48theorem  ⊢  
 proveit.numbers.multiplication.mult_rational_pos_closure_bin
49instantiation93, 91, 70  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
51axiom  ⊢  
 proveit.logic.equality.equals_transitivity
52instantiation54, 55  ⊢  
  : , : , :
53instantiation56, 57, 58  ⊢  
  : , :
54axiom  ⊢  
 proveit.logic.equality.substitution
55instantiation59, 60, 90, 61*  ⊢  
  : , :
56theorem  ⊢  
 proveit.numbers.multiplication.commutation
57instantiation93, 74, 62  ⊢  
  : , : , :
58instantiation93, 74, 63  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
60instantiation93, 64, 65  ⊢  
  : , : , :
61instantiation66, 67  ⊢  
  :
62instantiation68, 69, 70  ⊢  
  : , : , :
63instantiation93, 82, 71  ⊢  
  : , : , :
64theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
65instantiation93, 72, 73  ⊢  
  : , : , :
66theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
67instantiation93, 74, 75  ⊢  
  : , : , :
68theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
69instantiation76, 77  ⊢  
  : , :
70axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
71instantiation93, 78, 79  ⊢  
  : , : , :
72theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
73instantiation93, 80, 81  ⊢  
  : , : , :
74theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
75instantiation93, 82, 83  ⊢  
  : , : , :
76theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
77theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
78theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
79instantiation84, 85, 86  ⊢  
  : , :
80theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
81instantiation93, 87, 92  ⊢  
  : , : , :
82theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
83instantiation93, 88, 89  ⊢  
  : , : , :
84theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
85instantiation93, 91, 90  ⊢  
  : , : , :
86instantiation93, 91, 92  ⊢  
  : , : , :
87theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
88theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
89instantiation93, 94, 95  ⊢  
  : , : , :
90theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
91theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
92theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
93theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
94theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
95theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements