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