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.numbers.divisibility.even__if__power_is_even
2	instantiation	108, 13, 90	⊢
	: , : , :
3	reference	34	⊢
4	instantiation	45, 5, 6	, , ,  ⊢
	: , : , :
5	instantiation	7, 8, 9, 10	⊢
	: , :
6	instantiation	45, 11, 12	, , ,  ⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.divisibility.left_factor_divisibility
8	instantiation	108, 103, 16	⊢
	: , : , :
9	instantiation	108, 13, 14	⊢
	: , : , :
10	instantiation	44, 110	⊢
	:
11	instantiation	15, 16, 17, 81, 18	, , ,  ⊢
	: , : , :
12	instantiation	19, 20, 97, 110, 21*	,  ⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
14	instantiation	22, 23, 55	⊢
	: , :
15	theorem		⊢
	proveit.numbers.exponentiation.exp_eq_real
16	instantiation	108, 91, 24	⊢
	: , : , :
17	instantiation	25, 30, 104	,  ⊢
	: , :
18	instantiation	26, 104, 30, 27, 28, 29*	, , ,  ⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.exponentiation.posnat_power_of_product
20	instantiation	108, 103, 30	⊢
	: , : , :
21	instantiation	31, 73, 32*	⊢
	:
22	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
23	instantiation	108, 33, 113	⊢
	: , : , :
24	instantiation	108, 98, 34	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
26	theorem		⊢
	proveit.numbers.multiplication.right_mult_eq_real
27	instantiation	35, 81, 104, 36	,  ⊢
	: , :
28	instantiation	37, 38	⊢
	: , :
29	instantiation	45, 39, 40	,  ⊢
	: , : , :
30	instantiation	108, 91, 41	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.exponentiation.square_abs_rational_simp
32	instantiation	42, 110, 43	⊢
	: , :
33	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
34	instantiation	108, 105, 55	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.division.div_real_closure
36	instantiation	44, 113	⊢
	:
37	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
38	assumption		⊢
39	instantiation	45, 46, 47	,  ⊢
	: , : , :
40	instantiation	48, 49, 50, 51	⊢
	: , : , : , :
41	instantiation	108, 52, 53	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.exponentiation.nth_power_of_nth_root
43	instantiation	54, 55	⊢
	:
44	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
45	theorem		⊢
	proveit.logic.equality.sub_right_side_into
46	instantiation	56, 70, 71, 57, 58	,  ⊢
	: , : , : , : , :
47	instantiation	78, 59, 60	⊢
	: , : , :
48	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
49	instantiation	87, 61	⊢
	: , : , :
50	instantiation	87, 62	⊢
	: , : , :
51	instantiation	96, 70	⊢
	:
52	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
53	instantiation	63, 64	⊢
	:
54	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
56	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
57	instantiation	108, 66, 65	⊢
	: , : , :
58	instantiation	108, 66, 67	⊢
	: , : , :
59	instantiation	87, 68	⊢
	: , : , :
60	instantiation	87, 69	⊢
	: , : , :
61	instantiation	89, 70	⊢
	:
62	instantiation	89, 71	⊢
	:
63	theorem		⊢
	proveit.numbers.absolute_value.abs_rational_nonzero_closure
64	instantiation	72, 73, 74	⊢
	:
65	instantiation	108, 75, 94	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
67	instantiation	108, 75, 76	⊢
	: , : , :
68	instantiation	87, 77	⊢
	: , : , :
69	instantiation	78, 79, 80	⊢
	: , : , :
70	instantiation	108, 103, 81	⊢
	: , : , :
71	instantiation	108, 103, 82	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_rational_is_rational_nonzero
73	assumption		⊢
74	instantiation	83, 95, 84	⊢
	: , :
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
76	instantiation	108, 101, 85	⊢
	: , : , :
77	instantiation	86, 97	⊢
	:
78	axiom		⊢
	proveit.logic.equality.equals_transitivity
79	instantiation	87, 88	⊢
	: , : , :
80	instantiation	89, 97	⊢
	:
81	instantiation	111, 112, 90	⊢
	: , : , :
82	instantiation	108, 91, 92	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
84	instantiation	93, 94, 95	⊢
	: , :
85	instantiation	108, 109, 113	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
87	axiom		⊢
	proveit.logic.equality.substitution
88	instantiation	96, 97	⊢
	:
89	theorem		⊢
	proveit.numbers.division.frac_one_denom
90	assumption		⊢
91	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
92	instantiation	108, 98, 99	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
94	instantiation	108, 101, 100	⊢
	: , : , :
95	instantiation	108, 101, 102	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
97	instantiation	108, 103, 104	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
99	instantiation	108, 105, 106	⊢
	: , : , :
100	instantiation	108, 109, 107	⊢
	: , : , :
101	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
102	instantiation	108, 109, 110	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
104	instantiation	111, 112, 113	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
106	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
107	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
108	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
109	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
110	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
111	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
112	instantiation	114, 115	⊢
	: , :
113	assumption		⊢
114	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
115	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements