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