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	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
2	instantiation	22, 76, 5, 6, 7*	⊢
	: , :
3	instantiation	8	⊢
	:
4	instantiation	9, 10	⊢
	: , :
5	instantiation	11, 57, 25	⊢
	: , :
6	instantiation	12, 125, 13, 43, 14	⊢
	: , :
7	instantiation	35, 15, 16	⊢
	: , : , :
8	axiom		⊢
	proveit.logic.equality.equals_reflexivity
9	theorem		⊢
	proveit.logic.equality.equals_reversal
10	instantiation	47, 17	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
12	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
13	instantiation	45	⊢
	: , :
14	instantiation	18, 25, 27	⊢
	:
15	instantiation	47, 19	⊢
	: , : , :
16	instantiation	35, 20, 21	⊢
	: , : , :
17	instantiation	22, 76, 25, 27, 23*	⊢
	: , :
18	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
19	instantiation	24, 57, 25, 60, 26, 27, 28*, 48*	⊢
	: , : , :
20	instantiation	29, 115, 125, 31, 33, 32, 76, 34, 50	⊢
	: , : , : , : , : , :
21	instantiation	30, 31, 125, 32, 33, 34, 50	⊢
	: , : , : , :
22	theorem		⊢
	proveit.numbers.division.div_as_mult
23	instantiation	35, 36, 37	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
25	instantiation	123, 102, 38	⊢
	: , : , :
26	instantiation	73, 97	⊢
	:
27	instantiation	39, 40, 41	⊢
	: , :
28	instantiation	42, 43, 95, 44*	⊢
	: , :
29	theorem		⊢
	proveit.numbers.multiplication.disassociation
30	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
31	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
32	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
33	instantiation	45	⊢
	: , :
34	instantiation	123, 102, 46	⊢
	: , : , :
35	axiom		⊢
	proveit.logic.equality.equals_transitivity
36	instantiation	47, 48	⊢
	: , : , :
37	instantiation	49, 50	⊢
	:
38	instantiation	51, 78, 125	⊢
	: , :
39	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
40	instantiation	123, 80, 52	⊢
	: , : , :
41	instantiation	123, 80, 53	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
43	instantiation	123, 54, 55	⊢
	: , : , :
44	instantiation	56, 57	⊢
	:
45	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
46	instantiation	123, 107, 58	⊢
	: , : , :
47	axiom		⊢
	proveit.logic.equality.substitution
48	instantiation	59, 64, 103, 60, 61, 62*	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
50	instantiation	63, 64, 65	⊢
	: , :
51	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
52	instantiation	123, 93, 74	⊢
	: , : , :
53	instantiation	123, 93, 66	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
55	instantiation	123, 67, 68	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
57	instantiation	123, 102, 69	⊢
	: , : , :
58	instantiation	123, 70, 71	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
60	instantiation	72, 88	⊢
	:
61	instantiation	73, 74	⊢
	:
62	instantiation	75, 90, 76, 77*	⊢
	: , :
63	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
64	instantiation	123, 102, 78	⊢
	: , : , :
65	instantiation	123, 102, 79	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
68	instantiation	123, 80, 81	⊢
	: , : , :
69	instantiation	123, 107, 82	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
71	instantiation	83, 84, 85	⊢
	: , :
72	theorem		⊢
	proveit.numbers.negation.real_closure
73	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
74	instantiation	86, 104, 87	⊢
	:
75	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
76	instantiation	123, 102, 88	⊢
	: , : , :
77	instantiation	89, 90	⊢
	:
78	instantiation	123, 107, 91	⊢
	: , : , :
79	instantiation	123, 107, 92	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
81	instantiation	123, 93, 97	⊢
	: , : , :
82	instantiation	123, 111, 94	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
84	instantiation	123, 96, 95	⊢
	: , : , :
85	instantiation	123, 96, 97	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
87	instantiation	98, 99, 100	⊢
	: , : , :
88	instantiation	123, 107, 101	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
90	instantiation	123, 102, 103	⊢
	: , : , :
91	instantiation	123, 111, 104	⊢
	: , : , :
92	instantiation	123, 111, 118	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
94	instantiation	123, 124, 105	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
96	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
97	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
98	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
99	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
100	instantiation	106, 113, 114, 110	⊢
	: , : , :
101	instantiation	123, 111, 113	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
103	instantiation	123, 107, 108	⊢
	: , : , :
104	instantiation	123, 109, 110	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
106	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
107	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
108	instantiation	123, 111, 122	⊢
	: , : , :
109	instantiation	112, 113, 114	⊢
	: , :
110	assumption		⊢
111	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
112	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
113	instantiation	123, 124, 115	⊢
	: , : , :
114	instantiation	116, 117, 118	⊢
	: , :
115	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
116	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
117	instantiation	123, 119, 120	⊢
	: , : , :
118	instantiation	121, 122	⊢
	:
119	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
120	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
121	theorem		⊢
	proveit.numbers.negation.int_closure
122	instantiation	123, 124, 125	⊢
	: , : , :
123	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
124	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
125	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements