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