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	reference	16	⊢
2	instantiation	122, 27, 127	⊢
	: , : , :
3	reference	48	⊢
4	instantiation	5, 22, 6, 7, 24	, , ,  ⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.divisibility.common_factor_elimination
6	instantiation	122, 117, 8	⊢
	: , : , :
7	instantiation	59, 9, 10	, , ,  ⊢
	: , : , :
8	instantiation	125, 126, 28	⊢
	: , : , :
9	instantiation	11, 12, 20	, , ,  ⊢
	: , : , :
10	instantiation	13, 22	⊢
	:
11	theorem		⊢
	proveit.logic.equality.sub_left_side_into
12	instantiation	14, 48, 17, 124, 15	, , ,  ⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.exponentiation.square_expansion
14	theorem		⊢
	proveit.numbers.divisibility.common_exponent_introduction
15	instantiation	16, 17, 48, 18	, , ,  ⊢
	: , :
16	theorem		⊢
	proveit.numbers.divisibility.even__if__power_is_even
17	instantiation	122, 27, 104	⊢
	: , : , :
18	instantiation	59, 19, 20	, , ,  ⊢
	: , : , :
19	instantiation	21, 22, 23, 24	⊢
	: , :
20	instantiation	59, 25, 26	, , ,  ⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.divisibility.left_factor_divisibility
22	instantiation	122, 117, 30	⊢
	: , : , :
23	instantiation	122, 27, 28	⊢
	: , : , :
24	instantiation	58, 124	⊢
	:
25	instantiation	29, 30, 31, 95, 32	, , ,  ⊢
	: , : , :
26	instantiation	33, 34, 111, 124, 35*	,  ⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
28	instantiation	36, 37, 69	⊢
	: , :
29	theorem		⊢
	proveit.numbers.exponentiation.exp_eq_real
30	instantiation	122, 105, 38	⊢
	: , : , :
31	instantiation	39, 44, 118	,  ⊢
	: , :
32	instantiation	40, 118, 44, 41, 42, 43*	, , ,  ⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.exponentiation.posnat_power_of_product
34	instantiation	122, 117, 44	⊢
	: , : , :
35	instantiation	45, 87, 46*	⊢
	:
36	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
37	instantiation	122, 47, 127	⊢
	: , : , :
38	instantiation	122, 112, 48	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
40	theorem		⊢
	proveit.numbers.multiplication.right_mult_eq_real
41	instantiation	49, 95, 118, 50	,  ⊢
	: , :
42	instantiation	51, 52	⊢
	: , :
43	instantiation	59, 53, 54	,  ⊢
	: , : , :
44	instantiation	122, 105, 55	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.exponentiation.square_abs_rational_simp
46	instantiation	56, 124, 57	⊢
	: , :
47	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
48	instantiation	122, 119, 69	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.division.div_real_closure
50	instantiation	58, 127	⊢
	:
51	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
52	assumption		⊢
53	instantiation	59, 60, 61	,  ⊢
	: , : , :
54	instantiation	62, 63, 64, 65	⊢
	: , : , : , :
55	instantiation	122, 66, 67	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.exponentiation.nth_power_of_nth_root
57	instantiation	68, 69	⊢
	:
58	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
59	theorem		⊢
	proveit.logic.equality.sub_right_side_into
60	instantiation	70, 84, 85, 71, 72	,  ⊢
	: , : , : , : , :
61	instantiation	92, 73, 74	⊢
	: , : , :
62	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
63	instantiation	101, 75	⊢
	: , : , :
64	instantiation	101, 76	⊢
	: , : , :
65	instantiation	110, 84	⊢
	:
66	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
67	instantiation	77, 78	⊢
	:
68	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
70	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
71	instantiation	122, 80, 79	⊢
	: , : , :
72	instantiation	122, 80, 81	⊢
	: , : , :
73	instantiation	101, 82	⊢
	: , : , :
74	instantiation	101, 83	⊢
	: , : , :
75	instantiation	103, 84	⊢
	:
76	instantiation	103, 85	⊢
	:
77	theorem		⊢
	proveit.numbers.absolute_value.abs_rational_nonzero_closure
78	instantiation	86, 87, 88	⊢
	:
79	instantiation	122, 89, 108	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
81	instantiation	122, 89, 90	⊢
	: , : , :
82	instantiation	101, 91	⊢
	: , : , :
83	instantiation	92, 93, 94	⊢
	: , : , :
84	instantiation	122, 117, 95	⊢
	: , : , :
85	instantiation	122, 117, 96	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_rational_is_rational_nonzero
87	assumption		⊢
88	instantiation	97, 109, 98	⊢
	: , :
89	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
90	instantiation	122, 115, 99	⊢
	: , : , :
91	instantiation	100, 111	⊢
	:
92	axiom		⊢
	proveit.logic.equality.equals_transitivity
93	instantiation	101, 102	⊢
	: , : , :
94	instantiation	103, 111	⊢
	:
95	instantiation	125, 126, 104	⊢
	: , : , :
96	instantiation	122, 105, 106	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
98	instantiation	107, 108, 109	⊢
	: , :
99	instantiation	122, 123, 127	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
101	axiom		⊢
	proveit.logic.equality.substitution
102	instantiation	110, 111	⊢
	:
103	theorem		⊢
	proveit.numbers.division.frac_one_denom
104	assumption		⊢
105	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
106	instantiation	122, 112, 113	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
108	instantiation	122, 115, 114	⊢
	: , : , :
109	instantiation	122, 115, 116	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
111	instantiation	122, 117, 118	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
113	instantiation	122, 119, 120	⊢
	: , : , :
114	instantiation	122, 123, 121	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
116	instantiation	122, 123, 124	⊢
	: , : , :
117	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
118	instantiation	125, 126, 127	⊢
	: , : , :
119	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
120	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
121	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
122	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
123	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
124	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
125	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
126	instantiation	128, 129	⊢
	: , :
127	assumption		⊢
128	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
129	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements