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	theorem		⊢
	proveit.logic.sets.membership.fold_not_in_set
2	instantiation	3, 4, 5, 6	⊢
	: , :
3	theorem		⊢
	proveit.logic.booleans.implication.modus_tollens_denial
4	instantiation	7	⊢
	:
5	deduction	8	⊢
6	theorem		⊢
	proveit.logic.booleans.negation.not_false
7	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_membership_is_bool
8	modus ponens	9, 10	⊢
9	instantiation	11, 12, 13, 151	⊢
	: , : , : , : , : , :
10	instantiation	23, 14, 15	⊢
	: , :
11	theorem		⊢
	proveit.logic.booleans.quantification.existence.skolem_elim
12	instantiation	16	⊢
	: , :
13	instantiation	16	⊢
	: , :
14	instantiation	17, 94	⊢
	:
15	generalization	18	⊢
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
17	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.reduced_nat_pos_ratio
18	deduction	19	, ,  ⊢
19	instantiation	20, 21, 22	, , ,  ⊢
	:
20	theorem		⊢
	proveit.logic.booleans.negation.negation_contradiction
21	instantiation	23, 42, 24	, , ,  ⊢
	: , :
22	instantiation	25, 151, 26	, ,  ⊢
	:
23	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
24	instantiation	43, 27, 75, 28	, , ,  ⊢
	: , :
25	instantiation	29, 131, 154, 30	, ,  ⊢
	: , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
27	instantiation	149, 54, 154	⊢
	: , : , :
28	instantiation	31, 49, 32, 33, 51	, , ,  ⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.divisibility.GCD_one_def
30	instantiation	34, 79	⊢
	: , :
31	theorem		⊢
	proveit.numbers.divisibility.common_factor_elimination
32	instantiation	149, 144, 35	⊢
	: , : , :
33	instantiation	86, 36, 37	, , ,  ⊢
	: , : , :
34	theorem		⊢
	proveit.logic.booleans.conjunction.right_from_and
35	instantiation	152, 153, 55	⊢
	: , : , :
36	instantiation	38, 39, 47	, , ,  ⊢
	: , : , :
37	instantiation	40, 49	⊢
	:
38	theorem		⊢
	proveit.logic.equality.sub_left_side_into
39	instantiation	41, 75, 44, 151, 42	, , ,  ⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.exponentiation.square_expansion
41	theorem		⊢
	proveit.numbers.divisibility.common_exponent_introduction
42	instantiation	43, 44, 75, 45	, , ,  ⊢
	: , :
43	theorem		⊢
	proveit.numbers.divisibility.even__if__power_is_even
44	instantiation	149, 54, 131	⊢
	: , : , :
45	instantiation	86, 46, 47	, , ,  ⊢
	: , : , :
46	instantiation	48, 49, 50, 51	⊢
	: , :
47	instantiation	86, 52, 53	, , ,  ⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.divisibility.left_factor_divisibility
49	instantiation	149, 144, 57	⊢
	: , : , :
50	instantiation	149, 54, 55	⊢
	: , : , :
51	instantiation	85, 151	⊢
	:
52	instantiation	56, 57, 58, 122, 59	, , ,  ⊢
	: , : , :
53	instantiation	60, 61, 138, 151, 62*	,  ⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
55	instantiation	63, 64, 96	⊢
	: , :
56	theorem		⊢
	proveit.numbers.exponentiation.exp_eq_real
57	instantiation	149, 132, 65	⊢
	: , : , :
58	instantiation	66, 71, 145	,  ⊢
	: , :
59	instantiation	67, 145, 71, 68, 69, 70*	, , ,  ⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.exponentiation.posnat_power_of_product
61	instantiation	149, 144, 71	⊢
	: , : , :
62	instantiation	72, 114, 73*	⊢
	:
63	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
64	instantiation	149, 74, 154	⊢
	: , : , :
65	instantiation	149, 139, 75	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
67	theorem		⊢
	proveit.numbers.multiplication.right_mult_eq_real
68	instantiation	76, 122, 145, 77	,  ⊢
	: , :
69	instantiation	78, 79	⊢
	: , :
70	instantiation	86, 80, 81	,  ⊢
	: , : , :
71	instantiation	149, 132, 82	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.exponentiation.square_abs_rational_simp
73	instantiation	83, 151, 84	⊢
	: , :
74	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
75	instantiation	149, 146, 96	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.division.div_real_closure
77	instantiation	85, 154	⊢
	:
78	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
79	assumption		⊢
80	instantiation	86, 87, 88	,  ⊢
	: , : , :
81	instantiation	89, 90, 91, 92	⊢
	: , : , : , :
82	instantiation	149, 93, 94	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.exponentiation.nth_power_of_nth_root
84	instantiation	95, 96	⊢
	:
85	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
86	theorem		⊢
	proveit.logic.equality.sub_right_side_into
87	instantiation	97, 111, 112, 98, 99	,  ⊢
	: , : , : , : , :
88	instantiation	119, 100, 101	⊢
	: , : , :
89	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
90	instantiation	128, 102	⊢
	: , : , :
91	instantiation	128, 103	⊢
	: , : , :
92	instantiation	137, 111	⊢
	:
93	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
94	instantiation	104, 105	⊢
	:
95	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
96	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
97	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
98	instantiation	149, 107, 106	⊢
	: , : , :
99	instantiation	149, 107, 108	⊢
	: , : , :
100	instantiation	128, 109	⊢
	: , : , :
101	instantiation	128, 110	⊢
	: , : , :
102	instantiation	130, 111	⊢
	:
103	instantiation	130, 112	⊢
	:
104	theorem		⊢
	proveit.numbers.absolute_value.abs_rational_nonzero_closure
105	instantiation	113, 114, 115	⊢
	:
106	instantiation	149, 116, 135	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
108	instantiation	149, 116, 117	⊢
	: , : , :
109	instantiation	128, 118	⊢
	: , : , :
110	instantiation	119, 120, 121	⊢
	: , : , :
111	instantiation	149, 144, 122	⊢
	: , : , :
112	instantiation	149, 144, 123	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_rational_is_rational_nonzero
114	assumption		⊢
115	instantiation	124, 136, 125	⊢
	: , :
116	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
117	instantiation	149, 142, 126	⊢
	: , : , :
118	instantiation	127, 138	⊢
	:
119	axiom		⊢
	proveit.logic.equality.equals_transitivity
120	instantiation	128, 129	⊢
	: , : , :
121	instantiation	130, 138	⊢
	:
122	instantiation	152, 153, 131	⊢
	: , : , :
123	instantiation	149, 132, 133	⊢
	: , : , :
124	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
125	instantiation	134, 135, 136	⊢
	: , :
126	instantiation	149, 150, 154	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
128	axiom		⊢
	proveit.logic.equality.substitution
129	instantiation	137, 138	⊢
	:
130	theorem		⊢
	proveit.numbers.division.frac_one_denom
131	assumption		⊢
132	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
133	instantiation	149, 139, 140	⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
135	instantiation	149, 142, 141	⊢
	: , : , :
136	instantiation	149, 142, 143	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
138	instantiation	149, 144, 145	⊢
	: , : , :
139	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
140	instantiation	149, 146, 147	⊢
	: , : , :
141	instantiation	149, 150, 148	⊢
	: , : , :
142	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
143	instantiation	149, 150, 151	⊢
	: , : , :
144	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
145	instantiation	152, 153, 154	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
147	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
148	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
149	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
150	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
151	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
152	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
153	instantiation	155, 156	⊢
	: , :
154	assumption		⊢
155	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
156	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements