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