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	deduction	1	, ,  ⊢
1	instantiation	2, 3, 4	, , ,  ⊢
	:
2	theorem		⊢
	proveit.logic.booleans.negation.negation_contradiction
3	instantiation	5, 24, 6	, , ,  ⊢
	: , :
4	instantiation	7, 133, 8	, ,  ⊢
	:
5	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
6	instantiation	25, 9, 57, 10	, , ,  ⊢
	: , :
7	instantiation	11, 113, 136, 12	, ,  ⊢
	: , :
8	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
9	instantiation	131, 36, 136	⊢
	: , : , :
10	instantiation	13, 31, 14, 15, 33	, , ,  ⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.divisibility.GCD_one_def
12	instantiation	16, 61	⊢
	: , :
13	theorem		⊢
	proveit.numbers.divisibility.common_factor_elimination
14	instantiation	131, 126, 17	⊢
	: , : , :
15	instantiation	68, 18, 19	, , ,  ⊢
	: , : , :
16	theorem		⊢
	proveit.logic.booleans.conjunction.right_from_and
17	instantiation	134, 135, 37	⊢
	: , : , :
18	instantiation	20, 21, 29	, , ,  ⊢
	: , : , :
19	instantiation	22, 31	⊢
	:
20	theorem		⊢
	proveit.logic.equality.sub_left_side_into
21	instantiation	23, 57, 26, 133, 24	, , ,  ⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.exponentiation.square_expansion
23	theorem		⊢
	proveit.numbers.divisibility.common_exponent_introduction
24	instantiation	25, 26, 57, 27	, , ,  ⊢
	: , :
25	theorem		⊢
	proveit.numbers.divisibility.even__if__power_is_even
26	instantiation	131, 36, 113	⊢
	: , : , :
27	instantiation	68, 28, 29	, , ,  ⊢
	: , : , :
28	instantiation	30, 31, 32, 33	⊢
	: , :
29	instantiation	68, 34, 35	, , ,  ⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.divisibility.left_factor_divisibility
31	instantiation	131, 126, 39	⊢
	: , : , :
32	instantiation	131, 36, 37	⊢
	: , : , :
33	instantiation	67, 133	⊢
	:
34	instantiation	38, 39, 40, 104, 41	, , ,  ⊢
	: , : , :
35	instantiation	42, 43, 120, 133, 44*	,  ⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
37	instantiation	45, 46, 78	⊢
	: , :
38	theorem		⊢
	proveit.numbers.exponentiation.exp_eq_real
39	instantiation	131, 114, 47	⊢
	: , : , :
40	instantiation	48, 53, 127	,  ⊢
	: , :
41	instantiation	49, 127, 53, 50, 51, 52*	, , ,  ⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.exponentiation.posnat_power_of_product
43	instantiation	131, 126, 53	⊢
	: , : , :
44	instantiation	54, 96, 55*	⊢
	:
45	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
46	instantiation	131, 56, 136	⊢
	: , : , :
47	instantiation	131, 121, 57	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
49	theorem		⊢
	proveit.numbers.multiplication.right_mult_eq_real
50	instantiation	58, 104, 127, 59	,  ⊢
	: , :
51	instantiation	60, 61	⊢
	: , :
52	instantiation	68, 62, 63	,  ⊢
	: , : , :
53	instantiation	131, 114, 64	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.exponentiation.square_abs_rational_simp
55	instantiation	65, 133, 66	⊢
	: , :
56	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
57	instantiation	131, 128, 78	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.division.div_real_closure
59	instantiation	67, 136	⊢
	:
60	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
61	assumption		⊢
62	instantiation	68, 69, 70	,  ⊢
	: , : , :
63	instantiation	71, 72, 73, 74	⊢
	: , : , : , :
64	instantiation	131, 75, 76	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.exponentiation.nth_power_of_nth_root
66	instantiation	77, 78	⊢
	:
67	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
68	theorem		⊢
	proveit.logic.equality.sub_right_side_into
69	instantiation	79, 93, 94, 80, 81	,  ⊢
	: , : , : , : , :
70	instantiation	101, 82, 83	⊢
	: , : , :
71	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
72	instantiation	110, 84	⊢
	: , : , :
73	instantiation	110, 85	⊢
	: , : , :
74	instantiation	119, 93	⊢
	:
75	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
76	instantiation	86, 87	⊢
	:
77	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
78	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
79	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
80	instantiation	131, 89, 88	⊢
	: , : , :
81	instantiation	131, 89, 90	⊢
	: , : , :
82	instantiation	110, 91	⊢
	: , : , :
83	instantiation	110, 92	⊢
	: , : , :
84	instantiation	112, 93	⊢
	:
85	instantiation	112, 94	⊢
	:
86	theorem		⊢
	proveit.numbers.absolute_value.abs_rational_nonzero_closure
87	instantiation	95, 96, 97	⊢
	:
88	instantiation	131, 98, 117	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
90	instantiation	131, 98, 99	⊢
	: , : , :
91	instantiation	110, 100	⊢
	: , : , :
92	instantiation	101, 102, 103	⊢
	: , : , :
93	instantiation	131, 126, 104	⊢
	: , : , :
94	instantiation	131, 126, 105	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_rational_is_rational_nonzero
96	assumption		⊢
97	instantiation	106, 118, 107	⊢
	: , :
98	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
99	instantiation	131, 124, 108	⊢
	: , : , :
100	instantiation	109, 120	⊢
	:
101	axiom		⊢
	proveit.logic.equality.equals_transitivity
102	instantiation	110, 111	⊢
	: , : , :
103	instantiation	112, 120	⊢
	:
104	instantiation	134, 135, 113	⊢
	: , : , :
105	instantiation	131, 114, 115	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
107	instantiation	116, 117, 118	⊢
	: , :
108	instantiation	131, 132, 136	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
110	axiom		⊢
	proveit.logic.equality.substitution
111	instantiation	119, 120	⊢
	:
112	theorem		⊢
	proveit.numbers.division.frac_one_denom
113	assumption		⊢
114	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
115	instantiation	131, 121, 122	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
117	instantiation	131, 124, 123	⊢
	: , : , :
118	instantiation	131, 124, 125	⊢
	: , : , :
119	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
120	instantiation	131, 126, 127	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
122	instantiation	131, 128, 129	⊢
	: , : , :
123	instantiation	131, 132, 130	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
125	instantiation	131, 132, 133	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
127	instantiation	134, 135, 136	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
129	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
130	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
131	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
132	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
133	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
134	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
135	instantiation	137, 138	⊢
	: , :
136	assumption		⊢
137	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
138	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements