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, 70	⊢
	: , :
4	instantiation	7, 70	⊢
	: , :
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	,  ⊢
	: , :
11	theorem		⊢
	proveit.numbers.multiplication.commutation
12	instantiation	15, 16, 14	,  ⊢
	: , :
13	instantiation	15, 16, 17	⊢
	: , :
14	instantiation	34, 18, 19	,  ⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
16	instantiation	85, 60, 20	⊢
	: , : , :
17	instantiation	34, 21, 22	⊢
	: , : , :
18	instantiation	52, 37, 23	,  ⊢
	: , :
19	instantiation	28, 24, 25	,  ⊢
	: , : , :
20	instantiation	85, 65, 26	⊢
	: , : , :
21	instantiation	52, 37, 27	⊢
	: , :
22	instantiation	28, 29, 30	⊢
	: , : , :
23	instantiation	34, 31, 32	,  ⊢
	: , : , :
24	instantiation	43, 87, 38, 44, 33, 45, 37, 53, 54, 41	,  ⊢
	: , : , : , : , : , :
25	instantiation	43, 44, 82, 38, 45, 39, 33, 48, 49, 53, 54, 41	,  ⊢
	: , : , : , : , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
27	instantiation	34, 35, 36	⊢
	: , : , :
28	axiom		⊢
	proveit.logic.equality.equals_transitivity
29	instantiation	43, 87, 38, 44, 40, 45, 37, 53, 54, 47	⊢
	: , : , : , : , : , :
30	instantiation	43, 44, 82, 38, 45, 39, 40, 48, 49, 53, 54, 47	⊢
	: , : , : , : , : , :
31	instantiation	52, 42, 41	,  ⊢
	: , :
32	instantiation	43, 44, 82, 87, 45, 46, 53, 54, 41	,  ⊢
	: , : , : , : , : , :
33	instantiation	50	⊢
	: , : , :
34	theorem		⊢
	proveit.logic.equality.sub_right_side_into
35	instantiation	52, 42, 47	⊢
	: , :
36	instantiation	43, 44, 82, 87, 45, 46, 53, 54, 47	⊢
	: , : , : , : , : , :
37	instantiation	52, 48, 49	⊢
	: , :
38	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
39	instantiation	55	⊢
	: , :
40	instantiation	50	⊢
	: , : , :
41	instantiation	85, 60, 51	,  ⊢
	: , : , :
42	instantiation	52, 53, 54	⊢
	: , :
43	theorem		⊢
	proveit.numbers.multiplication.disassociation
44	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
45	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
46	instantiation	55	⊢
	: , :
47	instantiation	85, 60, 56	⊢
	: , : , :
48	instantiation	85, 60, 57	⊢
	: , : , :
49	instantiation	85, 60, 58	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
51	instantiation	85, 63, 59	,  ⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
53	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
54	instantiation	85, 60, 61	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
56	instantiation	85, 63, 62	⊢
	: , : , :
57	instantiation	85, 63, 64	⊢
	: , : , :
58	instantiation	85, 65, 66	⊢
	: , : , :
59	instantiation	85, 68, 67	,  ⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
61	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
62	instantiation	85, 68, 75	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
64	instantiation	85, 68, 78	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
67	instantiation	85, 69, 70	,  ⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
69	instantiation	71, 72, 73	⊢
	: , :
70	assumption		⊢
71	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
72	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
73	instantiation	74, 75, 76	⊢
	: , :
74	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
75	instantiation	77, 78, 79	⊢
	: , :
76	instantiation	80, 81	⊢
	:
77	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
78	instantiation	85, 86, 82	⊢
	: , : , :
79	instantiation	85, 83, 84	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.negation.int_closure
81	instantiation	85, 86, 87	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
83	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
84	assumption		⊢
85	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
86	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
87	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements