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	generalization	1	⊢
1	instantiation	2, 3, 4, 5	,  ⊢
	: , : , : , :
2	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
3	instantiation	6, 15, 104, 52, 32, 53, 11	,  ⊢
	: , : , : , : , : , :
4	instantiation	7, 104, 109, 15, 32, 11	,  ⊢
	: , : , : , : , :
5	instantiation	8, 9, 15, 10, 11, 12*	,  ⊢
	: , : , :
6	theorem		⊢
	proveit.physics.quantum.algebra.scalar_mult_absorption
7	theorem		⊢
	proveit.physics.quantum.algebra.qmult_pulling_scalar_out_front
8	theorem		⊢
	proveit.physics.quantum.algebra.scalar_mult_factorization
9	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
10	instantiation	58	⊢
	: , : , :
11	instantiation	21, 13, 23	,  ⊢
	: , : , :
12	instantiation	14, 15, 16	,  ⊢
	: , :
13	instantiation	17, 60, 61, 28, 29	,  ⊢
	: , : , : , :
14	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
15	instantiation	18, 19, 20	⊢
	: , :
16	instantiation	21, 22, 23	,  ⊢
	: , : , :
17	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_in_QmultCodomain
18	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
19	instantiation	107, 78, 24	⊢
	: , : , :
20	instantiation	40, 25, 26	⊢
	: , : , :
21	theorem		⊢
	proveit.logic.equality.sub_left_side_into
22	instantiation	27, 60, 61, 28, 29	,  ⊢
	: , : , : , :
23	instantiation	30, 31, 32	⊢
	: , : , :
24	instantiation	107, 83, 33	⊢
	: , : , :
25	instantiation	65, 43, 34	⊢
	: , :
26	instantiation	35, 36, 37	⊢
	: , : , :
27	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
28	instantiation	59, 60, 61, 38	⊢
	: , : , :
29	instantiation	39, 106, 92	⊢
	: , :
30	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
31	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
32	instantiation	68	⊢
	: , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
34	instantiation	40, 41, 42	⊢
	: , : , :
35	axiom		⊢
	proveit.logic.equality.equals_transitivity
36	instantiation	51, 109, 44, 52, 46, 53, 43, 66, 67, 55	⊢
	: , : , : , : , : , :
37	instantiation	51, 52, 104, 44, 53, 45, 46, 56, 57, 66, 67, 55	⊢
	: , : , : , : , : , :
38	instantiation	47, 60, 61, 48, 49	⊢
	: , : , : , : , :
39	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
40	theorem		⊢
	proveit.logic.equality.sub_right_side_into
41	instantiation	65, 50, 55	⊢
	: , :
42	instantiation	51, 52, 104, 109, 53, 54, 66, 67, 55	⊢
	: , : , : , : , : , :
43	instantiation	65, 56, 57	⊢
	: , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
45	instantiation	68	⊢
	: , :
46	instantiation	58	⊢
	: , : , :
47	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
48	instantiation	59, 60, 61, 62	⊢
	: , : , :
49	instantiation	63, 86, 64	⊢
	: , : , :
50	instantiation	65, 66, 67	⊢
	: , :
51	theorem		⊢
	proveit.numbers.multiplication.disassociation
52	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
53	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
54	instantiation	68	⊢
	: , :
55	instantiation	107, 78, 69	⊢
	: , : , :
56	instantiation	107, 78, 70	⊢
	: , : , :
57	instantiation	107, 78, 71	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
59	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
60	instantiation	72, 86	⊢
	:
61	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
62	instantiation	73, 106, 74	⊢
	: , :
63	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
64	instantiation	75, 76, 77	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
66	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
67	instantiation	107, 78, 79	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
69	instantiation	107, 81, 80	⊢
	: , : , :
70	instantiation	107, 81, 82	⊢
	: , : , :
71	instantiation	107, 83, 84	⊢
	: , : , :
72	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
73	theorem		⊢
	proveit.physics.quantum.algebra.num_bra_is_lin_map
74	assumption		⊢
75	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
76	instantiation	85, 86	⊢
	:
77	instantiation	87, 106	⊢
	:
78	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
79	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
80	instantiation	107, 89, 88	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
82	instantiation	107, 89, 100	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
84	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
85	theorem		⊢
	proveit.linear_algebra.matrices.unitaries_are_matrices
86	instantiation	90, 104, 101	⊢
	: , :
87	theorem		⊢
	proveit.physics.quantum.QFT.invFT_is_unitary
88	instantiation	107, 91, 92	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
90	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
91	instantiation	93, 94, 95	⊢
	: , :
92	assumption		⊢
93	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
94	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
95	instantiation	96, 97, 98	⊢
	: , :
96	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
97	instantiation	99, 100, 101	⊢
	: , :
98	instantiation	102, 103	⊢
	:
99	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
100	instantiation	107, 108, 104	⊢
	: , : , :
101	instantiation	107, 105, 106	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.negation.int_closure
103	instantiation	107, 108, 109	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
105	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
106	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
107	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
108	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
109	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements