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