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	axiom		⊢
	proveit.logic.equality.substitution
2	modus ponens	5, 6	⊢
3	instantiation	7, 101	⊢
	: , :
4	instantiation	7, 101	⊢
	: , :
5	instantiation	8, 9	⊢
	: , : , : , : , : , : , :
6	generalization	10	⊢
7	theorem		⊢
	proveit.core_expr_types.conditionals.satisfied_condition_reduction
8	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
9	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
10	instantiation	11, 12, 13, 14	,  ⊢
	: , : , : , :
11	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
12	instantiation	15, 24, 113, 61, 41, 62, 20	,  ⊢
	: , : , : , : , : , :
13	instantiation	16, 113, 118, 24, 41, 20	,  ⊢
	: , : , : , : , :
14	instantiation	17, 18, 24, 19, 20, 21*	,  ⊢
	: , : , :
15	theorem		⊢
	proveit.physics.quantum.algebra.scalar_mult_absorption
16	theorem		⊢
	proveit.physics.quantum.algebra.qmult_pulling_scalar_out_front
17	theorem		⊢
	proveit.physics.quantum.algebra.scalar_mult_factorization
18	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
19	instantiation	67	⊢
	: , : , :
20	instantiation	30, 22, 32	,  ⊢
	: , : , :
21	instantiation	23, 24, 25	,  ⊢
	: , :
22	instantiation	26, 69, 70, 37, 38	,  ⊢
	: , : , : , :
23	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
24	instantiation	27, 28, 29	⊢
	: , :
25	instantiation	30, 31, 32	,  ⊢
	: , : , :
26	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_in_QmultCodomain
27	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
28	instantiation	116, 87, 33	⊢
	: , : , :
29	instantiation	49, 34, 35	⊢
	: , : , :
30	theorem		⊢
	proveit.logic.equality.sub_left_side_into
31	instantiation	36, 69, 70, 37, 38	,  ⊢
	: , : , : , :
32	instantiation	39, 40, 41	⊢
	: , : , :
33	instantiation	116, 92, 42	⊢
	: , : , :
34	instantiation	74, 52, 43	⊢
	: , :
35	instantiation	44, 45, 46	⊢
	: , : , :
36	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_ket_is_ket
37	instantiation	68, 69, 70, 47	⊢
	: , : , :
38	instantiation	48, 115, 101	⊢
	: , :
39	axiom		⊢
	proveit.physics.quantum.algebra.multi_qmult_def
40	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
41	instantiation	77	⊢
	: , :
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
43	instantiation	49, 50, 51	⊢
	: , : , :
44	axiom		⊢
	proveit.logic.equality.equals_transitivity
45	instantiation	60, 118, 53, 61, 55, 62, 52, 75, 76, 64	⊢
	: , : , : , : , : , :
46	instantiation	60, 61, 113, 53, 62, 54, 55, 65, 66, 75, 76, 64	⊢
	: , : , : , : , : , :
47	instantiation	56, 69, 70, 57, 58	⊢
	: , : , : , : , :
48	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_in_register_space
49	theorem		⊢
	proveit.logic.equality.sub_right_side_into
50	instantiation	74, 59, 64	⊢
	: , :
51	instantiation	60, 61, 113, 118, 62, 63, 75, 76, 64	⊢
	: , : , : , : , : , :
52	instantiation	74, 65, 66	⊢
	: , :
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
54	instantiation	77	⊢
	: , :
55	instantiation	67	⊢
	: , : , :
56	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_op_is_op
57	instantiation	68, 69, 70, 71	⊢
	: , : , :
58	instantiation	72, 95, 73	⊢
	: , : , :
59	instantiation	74, 75, 76	⊢
	: , :
60	theorem		⊢
	proveit.numbers.multiplication.disassociation
61	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
62	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
63	instantiation	77	⊢
	: , :
64	instantiation	116, 87, 78	⊢
	: , : , :
65	instantiation	116, 87, 79	⊢
	: , : , :
66	instantiation	116, 87, 80	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
68	theorem		⊢
	proveit.physics.quantum.algebra.qmult_op_is_linmap
69	instantiation	81, 95	⊢
	:
70	theorem		⊢
	proveit.linear_algebra.inner_products.complex_set_is_hilbert_space
71	instantiation	82, 115, 83	⊢
	: , :
72	theorem		⊢
	proveit.physics.quantum.algebra.qmult_matrix_is_linmap
73	instantiation	84, 85, 86	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
75	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
76	instantiation	116, 87, 88	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
78	instantiation	116, 90, 89	⊢
	: , : , :
79	instantiation	116, 90, 91	⊢
	: , : , :
80	instantiation	116, 92, 93	⊢
	: , : , :
81	theorem		⊢
	proveit.linear_algebra.inner_products.complex_vec_set_is_hilbert_space
82	theorem		⊢
	proveit.physics.quantum.algebra.num_bra_is_lin_map
83	assumption		⊢
84	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
85	instantiation	94, 95	⊢
	:
86	instantiation	96, 115	⊢
	:
87	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
88	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
89	instantiation	116, 98, 97	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
91	instantiation	116, 98, 109	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
93	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
94	theorem		⊢
	proveit.linear_algebra.matrices.unitaries_are_matrices
95	instantiation	99, 113, 110	⊢
	: , :
96	theorem		⊢
	proveit.physics.quantum.QFT.invFT_is_unitary
97	instantiation	116, 100, 101	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
99	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
100	instantiation	102, 103, 104	⊢
	: , :
101	assumption		⊢
102	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
103	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
104	instantiation	105, 106, 107	⊢
	: , :
105	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
106	instantiation	108, 109, 110	⊢
	: , :
107	instantiation	111, 112	⊢
	:
108	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
109	instantiation	116, 117, 113	⊢
	: , : , :
110	instantiation	116, 114, 115	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.negation.int_closure
112	instantiation	116, 117, 118	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
114	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
115	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
116	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
117	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
118	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements