Show the Proof

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

	step type	requirements	statement
0	instantiation	1, 2, 3, 4, 5	⊢
	: , : , : , :
1	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
2	instantiation	24, 6, 7, 8	⊢
	: , :
3	reference	10	⊢
4	reference	11	⊢
5	instantiation	9, 10, 11, 12	⊢
	: , : , :
6	instantiation	83, 64, 13	⊢
	: , : , :
7	instantiation	14, 57, 15	⊢
	: , :
8	instantiation	16, 17, 18	⊢
	: , : , :
9	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
10	instantiation	19, 20	⊢
	:
11	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
12	instantiation	21, 60, 22	⊢
	: , :
13	instantiation	83, 72, 23	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
15	instantiation	24, 47, 57, 34	⊢
	: , :
16	theorem		⊢
	proveit.logic.equality.sub_left_side_into
17	instantiation	25, 63, 26	⊢
	: , :
18	instantiation	44, 27	⊢
	: , : , :
19	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
20	instantiation	28, 85, 29	⊢
	: , :
21	theorem		⊢
	proveit.physics.quantum.algebra.num_bra_is_lin_map
22	assumption		⊢
23	instantiation	83, 78, 30	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.division.div_complex_closure
25	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
26	instantiation	83, 31, 32	⊢
	: , : , :
27	instantiation	33, 47, 57, 34, 35*	⊢
	: , :
28	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
29	instantiation	83, 36, 60	⊢
	: , : , :
30	instantiation	83, 84, 37	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
32	instantiation	38, 69, 39	⊢
	: , :
33	theorem		⊢
	proveit.numbers.division.div_as_mult
34	instantiation	40, 82	⊢
	:
35	instantiation	41, 42, 43	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
37	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
38	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
39	instantiation	83, 81, 60	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
41	axiom		⊢
	proveit.logic.equality.equals_transitivity
42	instantiation	44, 45	⊢
	: , : , :
43	instantiation	46, 47, 48	⊢
	: , :
44	axiom		⊢
	proveit.logic.equality.substitution
45	instantiation	49, 50, 80, 51*	⊢
	: , :
46	theorem		⊢
	proveit.numbers.multiplication.commutation
47	instantiation	83, 64, 52	⊢
	: , : , :
48	instantiation	83, 64, 53	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
50	instantiation	83, 54, 55	⊢
	: , : , :
51	instantiation	56, 57	⊢
	:
52	instantiation	58, 59, 60	⊢
	: , : , :
53	instantiation	83, 72, 61	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
55	instantiation	83, 62, 63	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
57	instantiation	83, 64, 65	⊢
	: , : , :
58	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
59	instantiation	66, 67	⊢
	: , :
60	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
61	instantiation	83, 68, 69	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
63	instantiation	83, 70, 71	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
65	instantiation	83, 72, 73	⊢
	: , : , :
66	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
68	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
69	instantiation	74, 75, 76	⊢
	: , :
70	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
71	instantiation	83, 77, 82	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
73	instantiation	83, 78, 79	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
75	instantiation	83, 81, 80	⊢
	: , : , :
76	instantiation	83, 81, 82	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
78	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
79	instantiation	83, 84, 85	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
81	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
82	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
83	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
84	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
85	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements