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	⊢
	: , : , :
1	axiom		⊢
	proveit.logic.equality.substitution
2	modus ponens	3, 4	⊢
3	instantiation	5, 6	⊢
	: , : , : , : , : , :
4	generalization	7	⊢
5	axiom		⊢
	proveit.core_expr_types.lambda_maps.lambda_substitution
6	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
7	instantiation	8, 9	⊢
	: , : , :
8	axiom		⊢
	proveit.core_expr_types.conditionals.conditional_substitution
9	deduction	10	⊢
10	instantiation	11, 12, 13	,  ⊢
	: , :
11	theorem		⊢
	proveit.numbers.multiplication.commutation
12	instantiation	15, 16, 14	⊢
	: , :
13	instantiation	15, 16, 17	,  ⊢
	: , :
14	instantiation	48, 18, 19	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
16	instantiation	100, 72, 20	⊢
	: , : , :
17	instantiation	21, 22	,  ⊢
	:
18	instantiation	65, 51, 23	⊢
	: , :
19	instantiation	42, 24, 25	⊢
	: , : , :
20	instantiation	100, 76, 26	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.negation.complex_closure
22	instantiation	27, 28, 29, 30	,  ⊢
	: , :
23	instantiation	48, 31, 32	⊢
	: , : , :
24	instantiation	57, 102, 52, 58, 33, 59, 51, 66, 47, 67	⊢
	: , : , : , : , : , :
25	instantiation	57, 58, 97, 52, 59, 53, 33, 62, 63, 66, 47, 67	⊢
	: , : , : , : , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
27	theorem		⊢
	proveit.numbers.division.div_complex_closure
28	instantiation	48, 34, 35	,  ⊢
	: , : , :
29	instantiation	100, 72, 36	⊢
	: , : , :
30	instantiation	37, 38	⊢
	:
31	instantiation	65, 39, 67	⊢
	: , :
32	instantiation	57, 58, 97, 102, 59, 40, 66, 47, 67	⊢
	: , : , : , : , : , :
33	instantiation	64	⊢
	: , : , :
34	instantiation	65, 51, 41	,  ⊢
	: , :
35	instantiation	42, 43, 44	,  ⊢
	: , : , :
36	instantiation	100, 78, 45	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
38	instantiation	46, 97, 94	⊢
	: , :
39	instantiation	65, 66, 47	⊢
	: , :
40	instantiation	68	⊢
	: , :
41	instantiation	48, 49, 50	,  ⊢
	: , : , :
42	axiom		⊢
	proveit.logic.equality.equals_transitivity
43	instantiation	57, 102, 52, 58, 54, 59, 51, 66, 67, 61	,  ⊢
	: , : , : , : , : , :
44	instantiation	57, 58, 97, 52, 59, 53, 54, 62, 63, 66, 67, 61	,  ⊢
	: , : , : , : , : , :
45	instantiation	100, 81, 90	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
47	instantiation	100, 72, 55	⊢
	: , : , :
48	theorem		⊢
	proveit.logic.equality.sub_right_side_into
49	instantiation	65, 56, 61	,  ⊢
	: , :
50	instantiation	57, 58, 97, 102, 59, 60, 66, 67, 61	,  ⊢
	: , : , : , : , : , :
51	instantiation	65, 62, 63	⊢
	: , :
52	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
53	instantiation	68	⊢
	: , :
54	instantiation	64	⊢
	: , : , :
55	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
56	instantiation	65, 66, 67	⊢
	: , :
57	theorem		⊢
	proveit.numbers.multiplication.disassociation
58	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
59	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
60	instantiation	68	⊢
	: , :
61	instantiation	100, 72, 69	⊢
	: , : , :
62	instantiation	100, 72, 70	⊢
	: , : , :
63	instantiation	100, 72, 71	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
65	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
66	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
67	instantiation	100, 72, 73	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
69	instantiation	100, 78, 74	⊢
	: , : , :
70	instantiation	100, 78, 75	⊢
	: , : , :
71	instantiation	100, 76, 77	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
73	instantiation	100, 78, 79	⊢
	: , : , :
74	instantiation	100, 81, 80	⊢
	: , : , :
75	instantiation	100, 81, 93	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
78	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
79	instantiation	100, 81, 82	⊢
	: , : , :
80	instantiation	100, 84, 83	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
82	instantiation	100, 84, 85	⊢
	: , : , :
83	assumption		⊢
84	instantiation	86, 87, 88	⊢
	: , :
85	assumption		⊢
86	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
87	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
88	instantiation	89, 90, 91	⊢
	: , :
89	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
90	instantiation	92, 93, 94	⊢
	: , :
91	instantiation	95, 96	⊢
	:
92	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
93	instantiation	100, 101, 97	⊢
	: , : , :
94	instantiation	100, 98, 99	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.negation.int_closure
96	instantiation	100, 101, 102	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
98	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
99	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
100	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
101	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
102	theorem		⊢
	proveit.numbers.numerals.decimals.nat1