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