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, 5*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.exponentiation.product_of_complex_powers
2	reference	24	⊢
3	instantiation	6, 14	⊢
	:
4	reference	15	⊢
5	instantiation	29, 7, 8	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.negation.complex_closure
7	instantiation	9, 10	⊢
	: , : , :
8	instantiation	11, 12	⊢
	:
9	axiom		⊢
	proveit.logic.equality.substitution
10	instantiation	13, 14, 15, 16	⊢
	: , :
11	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
12	instantiation	83, 60, 17	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_reverse
14	instantiation	35, 18, 19	⊢
	: , : , :
15	instantiation	35, 20, 21	⊢
	: , : , :
16	instantiation	22, 39, 85, 46, 23, 47, 49, 50, 54, 52, 55	⊢
	: , : , : , : , : , : , :
17	instantiation	83, 63, 24	⊢
	: , : , :
18	instantiation	53, 38, 25	⊢
	: , :
19	instantiation	29, 26, 27	⊢
	: , : , :
20	instantiation	53, 38, 28	⊢
	: , :
21	instantiation	29, 30, 31	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
23	instantiation	51	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
25	instantiation	35, 32, 33	⊢
	: , : , :
26	instantiation	45, 85, 39, 46, 34, 47, 38, 54, 52, 55	⊢
	: , : , : , : , : , :
27	instantiation	45, 46, 70, 39, 47, 40, 34, 49, 50, 54, 52, 55	⊢
	: , : , : , : , : , :
28	instantiation	35, 36, 37	⊢
	: , : , :
29	axiom		⊢
	proveit.logic.equality.equals_transitivity
30	instantiation	45, 85, 39, 46, 41, 47, 38, 54, 55, 52	⊢
	: , : , : , : , : , :
31	instantiation	45, 46, 70, 39, 47, 40, 41, 49, 50, 54, 55, 52	⊢
	: , : , : , : , : , :
32	instantiation	53, 42, 55	⊢
	: , :
33	instantiation	45, 46, 70, 85, 47, 43, 54, 52, 55	⊢
	: , : , : , : , : , :
34	instantiation	51	⊢
	: , : , :
35	theorem		⊢
	proveit.logic.equality.sub_right_side_into
36	instantiation	53, 44, 52	⊢
	: , :
37	instantiation	45, 46, 70, 85, 47, 48, 54, 55, 52	⊢
	: , : , : , : , : , :
38	instantiation	53, 49, 50	⊢
	: , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
40	instantiation	56	⊢
	: , :
41	instantiation	51	⊢
	: , : , :
42	instantiation	53, 54, 52	⊢
	: , :
43	instantiation	56	⊢
	: , :
44	instantiation	53, 54, 55	⊢
	: , :
45	theorem		⊢
	proveit.numbers.multiplication.disassociation
46	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
47	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
48	instantiation	56	⊢
	: , :
49	instantiation	83, 60, 57	⊢
	: , : , :
50	instantiation	83, 60, 58	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
52	instantiation	83, 60, 59	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
54	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
55	instantiation	83, 60, 61	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
57	instantiation	83, 65, 62	⊢
	: , : , :
58	instantiation	83, 63, 64	⊢
	: , : , :
59	instantiation	83, 65, 66	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
61	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
62	instantiation	83, 68, 67	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
66	instantiation	83, 68, 69	⊢
	: , : , :
67	instantiation	83, 84, 70	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
69	instantiation	83, 71, 72	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
71	instantiation	73, 74, 75	⊢
	: , :
72	assumption		⊢
73	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
74	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
75	instantiation	76, 77, 78	⊢
	: , :
76	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
77	instantiation	83, 79, 80	⊢
	: , : , :
78	instantiation	81, 82	⊢
	:
79	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
80	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
81	theorem		⊢
	proveit.numbers.negation.int_closure
82	instantiation	83, 84, 85	⊢
	: , : , :
83	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
84	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
85	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements