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	reference	69	⊢
2	instantiation	59, 3, 4	⊢
	: , : , :
3	instantiation	69, 5	⊢
	: , : , :
4	instantiation	51, 75, 6, 7, 8*	⊢
	: , :
5	instantiation	69, 9	⊢
	: , : , :
6	instantiation	10, 90	⊢
	:
7	instantiation	11, 97, 12	⊢
	: , :
8	instantiation	59, 13, 14	⊢
	: , : , :
9	instantiation	59, 15, 16	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.exponentiation.sqrt_complex_closure
11	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
12	instantiation	17, 18, 97	⊢
	: , :
13	instantiation	69, 19	⊢
	: , : , :
14	instantiation	20, 21	⊢
	:
15	instantiation	59, 22, 23	⊢
	: , : , :
16	instantiation	59, 24, 25	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
18	instantiation	119, 105, 26	⊢
	: , : , :
19	instantiation	27, 90, 86, 28, 52, 29*	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
21	instantiation	30, 90, 31	⊢
	: , :
22	instantiation	69, 32	⊢
	: , : , :
23	instantiation	69, 33	⊢
	: , : , :
24	instantiation	34, 65, 121, 109, 67, 35, 45, 78, 36	⊢
	: , : , : , : , : , :
25	instantiation	37, 45, 78, 38	⊢
	: , : , :
26	instantiation	119, 113, 116	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
28	instantiation	119, 107, 39	⊢
	: , : , :
29	instantiation	40, 78, 75, 68*	⊢
	: , :
30	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
31	instantiation	119, 98, 41	⊢
	: , : , :
32	instantiation	51, 63, 90, 52, 42*	⊢
	: , :
33	instantiation	69, 43	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.addition.disassociation
35	instantiation	76	⊢
	: , :
36	instantiation	44, 45	⊢
	:
37	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
38	instantiation	46	⊢
	:
39	instantiation	119, 114, 47	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.negation.pos_times_neg
41	instantiation	48, 86	⊢
	:
42	instantiation	59, 49, 50	⊢
	: , : , :
43	instantiation	51, 74, 90, 52, 53*	⊢
	: , :
44	theorem		⊢
	proveit.numbers.negation.complex_closure
45	instantiation	119, 98, 54	⊢
	: , : , :
46	axiom		⊢
	proveit.logic.equality.equals_reflexivity
47	instantiation	55, 102	⊢
	:
48	theorem		⊢
	proveit.numbers.negation.real_closure
49	instantiation	69, 70	⊢
	: , : , :
50	instantiation	59, 56, 57	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.division.div_as_mult
52	instantiation	58, 118	⊢
	:
53	instantiation	59, 60, 61	⊢
	: , : , :
54	instantiation	119, 107, 62	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.negation.int_closure
56	instantiation	71, 63, 78	⊢
	: , :
57	instantiation	64, 109, 121, 65, 66, 67, 78, 74, 75, 68*	⊢
	: , : , : , : , : , :
58	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
59	axiom		⊢
	proveit.logic.equality.equals_transitivity
60	instantiation	69, 70	⊢
	: , : , :
61	instantiation	71, 74, 78	⊢
	: , :
62	instantiation	119, 103, 72	⊢
	: , : , :
63	instantiation	73, 74, 75	⊢
	: , :
64	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
65	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
66	instantiation	76	⊢
	: , :
67	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
68	instantiation	77, 78	⊢
	:
69	axiom		⊢
	proveit.logic.equality.substitution
70	instantiation	79, 80, 116, 81*	⊢
	: , :
71	theorem		⊢
	proveit.numbers.multiplication.commutation
72	instantiation	82, 104, 83	⊢
	: , :
73	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
74	instantiation	119, 98, 84	⊢
	: , : , :
75	instantiation	119, 98, 85	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
77	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
78	instantiation	119, 98, 86	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
80	instantiation	119, 87, 88	⊢
	: , : , :
81	instantiation	89, 90	⊢
	:
82	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
83	instantiation	119, 117, 93	⊢
	: , : , :
84	instantiation	91, 92, 93	⊢
	: , : , :
85	instantiation	119, 107, 94	⊢
	: , : , :
86	instantiation	119, 107, 95	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
88	instantiation	119, 96, 97	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
90	instantiation	119, 98, 99	⊢
	: , : , :
91	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
92	instantiation	100, 101	⊢
	: , :
93	assumption		⊢
94	instantiation	119, 114, 102	⊢
	: , : , :
95	instantiation	119, 103, 104	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
97	instantiation	119, 105, 106	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
99	instantiation	119, 107, 108	⊢
	: , : , :
100	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
101	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
102	instantiation	119, 120, 109	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
104	instantiation	110, 111, 112	⊢
	: , :
105	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
106	instantiation	119, 113, 118	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
108	instantiation	119, 114, 115	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
110	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
111	instantiation	119, 117, 116	⊢
	: , : , :
112	instantiation	119, 117, 118	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
114	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
115	instantiation	119, 120, 121	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
117	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
118	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
119	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
120	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
121	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements