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	modus ponens	1, 2	⊢
1	instantiation	3, 4	⊢
	: , : , : , : , : , : , :
2	generalization	5	⊢
3	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
4	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
5	instantiation	6, 7, 8, 9	,  ⊢
	: , : , : , :
6	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
7	instantiation	10, 19, 108, 56, 36, 57, 15	,  ⊢
	: , : , : , : , : , :
8	instantiation	11, 108, 113, 19, 36, 15	,  ⊢
	: , : , : , : , :
9	instantiation	12, 13, 19, 14, 15, 16*	,  ⊢
	: , : , :
10	theorem		⊢
	proveit.physics.quantum.algebra.scalar_mult_absorption
11	theorem		⊢
	proveit.physics.quantum.algebra.qmult_pulling_scalar_out_front
12	theorem		⊢
	proveit.physics.quantum.algebra.scalar_mult_factorization
13	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
14	instantiation	62	⊢
	: , : , :
15	instantiation	25, 17, 27	,  ⊢
	: , : , :
16	instantiation	18, 19, 20	,  ⊢
	: , :
17	instantiation	21, 64, 65, 32, 33	,  ⊢
	: , : , : , :
18	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
19	instantiation	22, 23, 24	⊢
	: , :
20	instantiation	25, 26, 27	,  ⊢
	: , : , :
21	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_in_QmultCodomain
22	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
23	instantiation	111, 82, 28	⊢
	: , : , :
24	instantiation	44, 29, 30	⊢
	: , : , :
25	theorem		⊢
	proveit.logic.equality.sub_left_side_into
26	instantiation	31, 64, 65, 32, 33	,  ⊢
	: , : , : , :
27	instantiation	34, 35, 36	⊢
	: , : , :
28	instantiation	111, 87, 37	⊢
	: , : , :
29	instantiation	69, 47, 38	⊢
	: , :
30	instantiation	39, 40, 41	⊢
	: , : , :
31	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
32	instantiation	63, 64, 65, 42	⊢
	: , : , :
33	instantiation	43, 110, 96	⊢
	: , :
34	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
35	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
36	instantiation	72	⊢
	: , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
38	instantiation	44, 45, 46	⊢
	: , : , :
39	axiom		⊢
	proveit.logic.equality.equals_transitivity
40	instantiation	55, 113, 48, 56, 50, 57, 47, 70, 71, 59	⊢
	: , : , : , : , : , :
41	instantiation	55, 56, 108, 48, 57, 49, 50, 60, 61, 70, 71, 59	⊢
	: , : , : , : , : , :
42	instantiation	51, 64, 65, 52, 53	⊢
	: , : , : , : , :
43	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
44	theorem		⊢
	proveit.logic.equality.sub_right_side_into
45	instantiation	69, 54, 59	⊢
	: , :
46	instantiation	55, 56, 108, 113, 57, 58, 70, 71, 59	⊢
	: , : , : , : , : , :
47	instantiation	69, 60, 61	⊢
	: , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
49	instantiation	72	⊢
	: , :
50	instantiation	62	⊢
	: , : , :
51	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
52	instantiation	63, 64, 65, 66	⊢
	: , : , :
53	instantiation	67, 90, 68	⊢
	: , : , :
54	instantiation	69, 70, 71	⊢
	: , :
55	theorem		⊢
	proveit.numbers.multiplication.disassociation
56	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
57	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
58	instantiation	72	⊢
	: , :
59	instantiation	111, 82, 73	⊢
	: , : , :
60	instantiation	111, 82, 74	⊢
	: , : , :
61	instantiation	111, 82, 75	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
63	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
64	instantiation	76, 90	⊢
	:
65	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
66	instantiation	77, 110, 78	⊢
	: , :
67	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
68	instantiation	79, 80, 81	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
70	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
71	instantiation	111, 82, 83	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
73	instantiation	111, 85, 84	⊢
	: , : , :
74	instantiation	111, 85, 86	⊢
	: , : , :
75	instantiation	111, 87, 88	⊢
	: , : , :
76	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
77	theorem		⊢
	proveit.physics.quantum.algebra.num_bra_is_lin_map
78	assumption		⊢
79	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
80	instantiation	89, 90	⊢
	:
81	instantiation	91, 110	⊢
	:
82	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
83	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
84	instantiation	111, 93, 92	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
86	instantiation	111, 93, 104	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
88	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
89	theorem		⊢
	proveit.linear_algebra.matrices.unitaries_are_matrices
90	instantiation	94, 108, 105	⊢
	: , :
91	theorem		⊢
	proveit.physics.quantum.QFT.invFT_is_unitary
92	instantiation	111, 95, 96	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
94	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
95	instantiation	97, 98, 99	⊢
	: , :
96	assumption		⊢
97	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
98	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
99	instantiation	100, 101, 102	⊢
	: , :
100	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
101	instantiation	103, 104, 105	⊢
	: , :
102	instantiation	106, 107	⊢
	:
103	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
104	instantiation	111, 112, 108	⊢
	: , : , :
105	instantiation	111, 109, 110	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.negation.int_closure
107	instantiation	111, 112, 113	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
109	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
110	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
111	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
112	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
113	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements