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	⊢
	: , : , :
1	reference	11	⊢
2	reference	12	⊢
3	reference	13	⊢
4	instantiation	5, 6, 12, 13, 7	⊢
	: , : , : , :
5	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_complex_closure
6	instantiation	26, 8, 9, 10	⊢
	: , :
7	instantiation	11, 12, 13, 14	⊢
	: , : , :
8	instantiation	85, 66, 15	⊢
	: , : , :
9	instantiation	16, 59, 17	⊢
	: , :
10	instantiation	18, 19, 20	⊢
	: , : , :
11	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
12	instantiation	21, 22	⊢
	:
13	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
14	instantiation	23, 62, 24	⊢
	: , :
15	instantiation	85, 74, 25	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
17	instantiation	26, 49, 59, 36	⊢
	: , :
18	theorem		⊢
	proveit.logic.equality.sub_left_side_into
19	instantiation	27, 65, 28	⊢
	: , :
20	instantiation	46, 29	⊢
	: , : , :
21	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
22	instantiation	30, 87, 31	⊢
	: , :
23	theorem		⊢
	proveit.physics.quantum.algebra.num_bra_is_lin_map
24	assumption		⊢
25	instantiation	85, 80, 32	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.division.div_complex_closure
27	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
28	instantiation	85, 33, 34	⊢
	: , : , :
29	instantiation	35, 49, 59, 36, 37*	⊢
	: , :
30	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
31	instantiation	85, 38, 62	⊢
	: , : , :
32	instantiation	85, 86, 39	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
34	instantiation	40, 71, 41	⊢
	: , :
35	theorem		⊢
	proveit.numbers.division.div_as_mult
36	instantiation	42, 84	⊢
	:
37	instantiation	43, 44, 45	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
40	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
41	instantiation	85, 83, 62	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
43	axiom		⊢
	proveit.logic.equality.equals_transitivity
44	instantiation	46, 47	⊢
	: , : , :
45	instantiation	48, 49, 50	⊢
	: , :
46	axiom		⊢
	proveit.logic.equality.substitution
47	instantiation	51, 52, 82, 53*	⊢
	: , :
48	theorem		⊢
	proveit.numbers.multiplication.commutation
49	instantiation	85, 66, 54	⊢
	: , : , :
50	instantiation	85, 66, 55	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
52	instantiation	85, 56, 57	⊢
	: , : , :
53	instantiation	58, 59	⊢
	:
54	instantiation	60, 61, 62	⊢
	: , : , :
55	instantiation	85, 74, 63	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
57	instantiation	85, 64, 65	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
59	instantiation	85, 66, 67	⊢
	: , : , :
60	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
61	instantiation	68, 69	⊢
	: , :
62	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
63	instantiation	85, 70, 71	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
65	instantiation	85, 72, 73	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
67	instantiation	85, 74, 75	⊢
	: , : , :
68	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
69	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
70	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
71	instantiation	76, 77, 78	⊢
	: , :
72	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
73	instantiation	85, 79, 84	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
75	instantiation	85, 80, 81	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
77	instantiation	85, 83, 82	⊢
	: , : , :
78	instantiation	85, 83, 84	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
80	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
81	instantiation	85, 86, 87	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
83	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
84	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
85	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
86	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
87	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements