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, 128	⊢
	: , : , : , : , : , :
2	generalization	4	⊢
3	axiom		⊢
	proveit.core_expr_types.lambda_maps.lambda_substitution
4	instantiation	5, 6	⊢
	: , : , :
5	axiom		⊢
	proveit.core_expr_types.conditionals.conditional_substitution
6	deduction	7	⊢
7	instantiation	86, 152, 147, 87, 8, 88, 9, 10, 11	,  ⊢
	: , : , : , : , : , :
8	instantiation	103	⊢
	: , :
9	instantiation	21, 16, 12	⊢
	: , :
10	instantiation	37, 13, 14, 15	⊢
	: , :
11	instantiation	21, 16, 17	,  ⊢
	: , :
12	instantiation	72, 18, 19	⊢
	: , : , :
13	instantiation	150, 113, 20	⊢
	: , : , :
14	instantiation	21, 96, 22	⊢
	: , :
15	instantiation	23, 24, 25	⊢
	: , : , :
16	instantiation	150, 113, 26	⊢
	: , : , :
17	instantiation	27, 28	,  ⊢
	:
18	instantiation	100, 75, 29	⊢
	: , :
19	instantiation	61, 30, 31	⊢
	: , : , :
20	instantiation	150, 124, 32	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
22	instantiation	37, 70, 96, 47	⊢
	: , :
23	theorem		⊢
	proveit.logic.equality.sub_left_side_into
24	instantiation	33, 107, 34	⊢
	: , :
25	instantiation	67, 35	⊢
	: , : , :
26	instantiation	150, 116, 36	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.negation.complex_closure
28	instantiation	37, 38, 39, 40	,  ⊢
	: , :
29	instantiation	72, 41, 42	⊢
	: , : , :
30	instantiation	86, 152, 76, 87, 43, 88, 75, 101, 66, 102	⊢
	: , : , : , : , : , :
31	instantiation	86, 87, 147, 76, 88, 77, 43, 96, 91, 101, 66, 102	⊢
	: , : , : , : , : , :
32	instantiation	150, 131, 146	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
34	instantiation	150, 44, 45	⊢
	: , : , :
35	instantiation	46, 70, 96, 47, 48*	⊢
	: , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
37	theorem		⊢
	proveit.numbers.division.div_complex_closure
38	instantiation	72, 49, 50	,  ⊢
	: , : , :
39	instantiation	150, 113, 51	⊢
	: , : , :
40	instantiation	57, 52	⊢
	:
41	instantiation	100, 53, 102	⊢
	: , :
42	instantiation	86, 87, 147, 152, 88, 54, 101, 66, 102	⊢
	: , : , : , : , : , :
43	instantiation	92	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
45	instantiation	55, 112, 56	⊢
	: , :
46	theorem		⊢
	proveit.numbers.division.div_as_mult
47	instantiation	57, 130	⊢
	:
48	instantiation	61, 58, 59	⊢
	: , : , :
49	instantiation	100, 75, 60	,  ⊢
	: , :
50	instantiation	61, 62, 63	,  ⊢
	: , : , :
51	instantiation	150, 124, 64	⊢
	: , : , :
52	instantiation	65, 147, 144	⊢
	: , :
53	instantiation	100, 101, 66	⊢
	: , :
54	instantiation	103	⊢
	: , :
55	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
56	instantiation	150, 129, 149	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
58	instantiation	67, 68	⊢
	: , : , :
59	instantiation	69, 70, 71	⊢
	: , :
60	instantiation	72, 73, 74	,  ⊢
	: , : , :
61	axiom		⊢
	proveit.logic.equality.equals_transitivity
62	instantiation	86, 152, 76, 87, 78, 88, 75, 101, 102, 90	,  ⊢
	: , : , : , : , : , :
63	instantiation	86, 87, 147, 76, 88, 77, 78, 96, 91, 101, 102, 90	,  ⊢
	: , : , : , : , : , :
64	instantiation	150, 131, 140	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
66	instantiation	150, 113, 79	⊢
	: , : , :
67	axiom		⊢
	proveit.logic.equality.substitution
68	instantiation	80, 81, 128, 82*	⊢
	: , :
69	theorem		⊢
	proveit.numbers.multiplication.commutation
70	instantiation	150, 113, 83	⊢
	: , : , :
71	instantiation	150, 113, 84	⊢
	: , : , :
72	theorem		⊢
	proveit.logic.equality.sub_right_side_into
73	instantiation	100, 85, 90	,  ⊢
	: , :
74	instantiation	86, 87, 147, 152, 88, 89, 101, 102, 90	,  ⊢
	: , : , : , : , : , :
75	instantiation	100, 96, 91	⊢
	: , :
76	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
77	instantiation	103	⊢
	: , :
78	instantiation	92	⊢
	: , : , :
79	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
80	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
81	instantiation	150, 93, 94	⊢
	: , : , :
82	instantiation	95, 96	⊢
	:
83	instantiation	97, 98, 149	⊢
	: , : , :
84	instantiation	150, 124, 99	⊢
	: , : , :
85	instantiation	100, 101, 102	⊢
	: , :
86	theorem		⊢
	proveit.numbers.multiplication.disassociation
87	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
88	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
89	instantiation	103	⊢
	: , :
90	instantiation	150, 113, 104	⊢
	: , : , :
91	instantiation	150, 113, 105	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
93	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
94	instantiation	150, 106, 107	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
96	instantiation	150, 113, 108	⊢
	: , : , :
97	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
98	instantiation	109, 110	⊢
	: , :
99	instantiation	150, 111, 112	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
101	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
102	instantiation	150, 113, 114	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
104	instantiation	150, 124, 115	⊢
	: , : , :
105	instantiation	150, 116, 117	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
107	instantiation	150, 118, 119	⊢
	: , : , :
108	instantiation	150, 124, 120	⊢
	: , : , :
109	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
110	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
111	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
112	instantiation	121, 122, 123	⊢
	: , :
113	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
114	instantiation	150, 124, 125	⊢
	: , : , :
115	instantiation	150, 131, 126	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
117	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
118	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
119	instantiation	150, 127, 130	⊢
	: , : , :
120	instantiation	150, 131, 143	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
122	instantiation	150, 129, 128	⊢
	: , : , :
123	instantiation	150, 129, 130	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
125	instantiation	150, 131, 132	⊢
	: , : , :
126	instantiation	150, 134, 133	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
128	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
129	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
130	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
131	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
132	instantiation	150, 134, 135	⊢
	: , : , :
133	assumption		⊢
134	instantiation	136, 137, 138	⊢
	: , :
135	assumption		⊢
136	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
137	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
138	instantiation	139, 140, 141	⊢
	: , :
139	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
140	instantiation	142, 143, 144	⊢
	: , :
141	instantiation	145, 146	⊢
	:
142	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
143	instantiation	150, 151, 147	⊢
	: , : , :
144	instantiation	150, 148, 149	⊢
	: , : , :
145	theorem		⊢
	proveit.numbers.negation.int_closure
146	instantiation	150, 151, 152	⊢
	: , : , :
147	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
148	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
149	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
150	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
151	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
152	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements