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