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, 5	, , ,  ⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.divisibility.common_exponent_introduction
2	reference	38	⊢
3	reference	7	⊢
4	reference	114	⊢
5	instantiation	6, 7, 38, 8	, , ,  ⊢
	: , :
6	theorem		⊢
	proveit.numbers.divisibility.even__if__power_is_even
7	instantiation	112, 17, 94	⊢
	: , : , :
8	instantiation	49, 9, 10	, , ,  ⊢
	: , : , :
9	instantiation	11, 12, 13, 14	⊢
	: , :
10	instantiation	49, 15, 16	, , ,  ⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.divisibility.left_factor_divisibility
12	instantiation	112, 107, 20	⊢
	: , : , :
13	instantiation	112, 17, 18	⊢
	: , : , :
14	instantiation	48, 114	⊢
	:
15	instantiation	19, 20, 21, 85, 22	, , ,  ⊢
	: , : , :
16	instantiation	23, 24, 101, 114, 25*	,  ⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
18	instantiation	26, 27, 59	⊢
	: , :
19	theorem		⊢
	proveit.numbers.exponentiation.exp_eq_real
20	instantiation	112, 95, 28	⊢
	: , : , :
21	instantiation	29, 34, 108	,  ⊢
	: , :
22	instantiation	30, 108, 34, 31, 32, 33*	, , ,  ⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.exponentiation.posnat_power_of_product
24	instantiation	112, 107, 34	⊢
	: , : , :
25	instantiation	35, 77, 36*	⊢
	:
26	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
27	instantiation	112, 37, 117	⊢
	: , : , :
28	instantiation	112, 102, 38	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
30	theorem		⊢
	proveit.numbers.multiplication.right_mult_eq_real
31	instantiation	39, 85, 108, 40	,  ⊢
	: , :
32	instantiation	41, 42	⊢
	: , :
33	instantiation	49, 43, 44	,  ⊢
	: , : , :
34	instantiation	112, 95, 45	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.exponentiation.square_abs_rational_simp
36	instantiation	46, 114, 47	⊢
	: , :
37	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
38	instantiation	112, 109, 59	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.division.div_real_closure
40	instantiation	48, 117	⊢
	:
41	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
42	assumption		⊢
43	instantiation	49, 50, 51	,  ⊢
	: , : , :
44	instantiation	52, 53, 54, 55	⊢
	: , : , : , :
45	instantiation	112, 56, 57	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.exponentiation.nth_power_of_nth_root
47	instantiation	58, 59	⊢
	:
48	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
49	theorem		⊢
	proveit.logic.equality.sub_right_side_into
50	instantiation	60, 74, 75, 61, 62	,  ⊢
	: , : , : , : , :
51	instantiation	82, 63, 64	⊢
	: , : , :
52	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
53	instantiation	91, 65	⊢
	: , : , :
54	instantiation	91, 66	⊢
	: , : , :
55	instantiation	100, 74	⊢
	:
56	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
57	instantiation	67, 68	⊢
	:
58	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
60	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
61	instantiation	112, 70, 69	⊢
	: , : , :
62	instantiation	112, 70, 71	⊢
	: , : , :
63	instantiation	91, 72	⊢
	: , : , :
64	instantiation	91, 73	⊢
	: , : , :
65	instantiation	93, 74	⊢
	:
66	instantiation	93, 75	⊢
	:
67	theorem		⊢
	proveit.numbers.absolute_value.abs_rational_nonzero_closure
68	instantiation	76, 77, 78	⊢
	:
69	instantiation	112, 79, 98	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
71	instantiation	112, 79, 80	⊢
	: , : , :
72	instantiation	91, 81	⊢
	: , : , :
73	instantiation	82, 83, 84	⊢
	: , : , :
74	instantiation	112, 107, 85	⊢
	: , : , :
75	instantiation	112, 107, 86	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_rational_is_rational_nonzero
77	assumption		⊢
78	instantiation	87, 99, 88	⊢
	: , :
79	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
80	instantiation	112, 105, 89	⊢
	: , : , :
81	instantiation	90, 101	⊢
	:
82	axiom		⊢
	proveit.logic.equality.equals_transitivity
83	instantiation	91, 92	⊢
	: , : , :
84	instantiation	93, 101	⊢
	:
85	instantiation	115, 116, 94	⊢
	: , : , :
86	instantiation	112, 95, 96	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
88	instantiation	97, 98, 99	⊢
	: , :
89	instantiation	112, 113, 117	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
91	axiom		⊢
	proveit.logic.equality.substitution
92	instantiation	100, 101	⊢
	:
93	theorem		⊢
	proveit.numbers.division.frac_one_denom
94	assumption		⊢
95	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
96	instantiation	112, 102, 103	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
98	instantiation	112, 105, 104	⊢
	: , : , :
99	instantiation	112, 105, 106	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
101	instantiation	112, 107, 108	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
103	instantiation	112, 109, 110	⊢
	: , : , :
104	instantiation	112, 113, 111	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
106	instantiation	112, 113, 114	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
108	instantiation	115, 116, 117	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
110	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
111	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
112	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
113	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
114	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
115	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
116	instantiation	118, 119	⊢
	: , :
117	assumption		⊢
118	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
119	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements