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	instantiation	77, 2, 3	, , ,  ⊢
	: , : , :
2	instantiation	31, 4, 5	, , ,  ⊢
	: , : , :
3	instantiation	43, 6	, ,  ⊢
	: , :
4	instantiation	31, 7, 8	, , ,  ⊢
	: , : , :
5	instantiation	25, 9, 10, 11, 12*	, ,  ⊢
	: , : , : , :
6	instantiation	31, 13, 14	, ,  ⊢
	: , : , :
7	instantiation	15, 16, 17	, , ,  ⊢
	: , : , :
8	instantiation	18, 98, 143, 99, 107, 119, 112, 19*, 20*	,  ⊢
	: , : , : , : , : , :
9	instantiation	22, 21	, ,  ⊢
	: , : , :
10	instantiation	22, 23	, ,  ⊢
	: , : , :
11	instantiation	43, 24	, ,  ⊢
	: , :
12	instantiation	25, 26, 27, 28	,  ⊢
	: , : , : , :
13	instantiation	43, 29	, ,  ⊢
	: , :
14	instantiation	30, 125, 124	⊢
	: , :
15	theorem		⊢
	proveit.logic.equality.sub_left_side_into
16	instantiation	31, 32, 33	,  ⊢
	: , : , :
17	instantiation	34, 35, 36, 112, 37*, 38*	, ,  ⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.multiplication.distribute_through_subtract
19	instantiation	81, 112	,  ⊢
	:
20	instantiation	39, 119, 110, 72, 40*, 41*	,  ⊢
	: , : , :
21	instantiation	43, 42	, ,  ⊢
	: , :
22	axiom		⊢
	proveit.logic.equality.substitution
23	instantiation	43, 44	, ,  ⊢
	: , :
24	instantiation	45, 143, 146, 98, 46, 99, 47, 80, 82	, ,  ⊢
	: , : , : , : , : , :
25	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
26	instantiation	89, 98, 146, 143, 99, 48, 107, 102, 82	,  ⊢
	: , : , : , : , : , :
27	instantiation	89, 146, 98, 48, 49, 99, 107, 102, 112, 103	,  ⊢
	: , : , : , : , : , :
28	instantiation	50, 143, 98, 99, 107, 112, 103	,  ⊢
	: , : , : , : , : , : , : , :
29	instantiation	65, 107, 70, 68, 69, 51*	, ,  ⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.addition.commutation
31	theorem		⊢
	proveit.logic.equality.sub_right_side_into
32	instantiation	52, 53, 130, 54, 55*	⊢
	: , : , : , :
33	assumption		⊢
34	theorem		⊢
	proveit.numbers.division.frac_cancel_left
35	instantiation	56, 68, 69	,  ⊢
	:
36	instantiation	144, 57, 58	⊢
	: , : , :
37	instantiation	59, 68	⊢
	:
38	instantiation	60, 112	,  ⊢
	:
39	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
40	instantiation	61, 119	⊢
	:
41	instantiation	77, 62, 63	⊢
	: , : , :
42	instantiation	65, 107, 80, 68, 69, 64*	, ,  ⊢
	: , : , :
43	theorem		⊢
	proveit.logic.equality.equals_reversal
44	instantiation	65, 107, 82, 68, 69, 66*	, ,  ⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
46	instantiation	111	⊢
	: , :
47	instantiation	67, 107, 68, 69	,  ⊢
	: , :
48	instantiation	111	⊢
	: , :
49	instantiation	111	⊢
	: , :
50	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general_rev
51	instantiation	81, 70	,  ⊢
	:
52	axiom		⊢
	proveit.numbers.summation.sum_split_last
53	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
54	instantiation	71, 72	⊢
	:
55	instantiation	77, 73, 74	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
57	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
58	instantiation	144, 75, 76	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
60	theorem		⊢
	proveit.numbers.division.frac_one_denom
61	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
62	instantiation	89, 143, 146, 98, 90, 99, 107, 125	⊢
	: , : , : , : , : , :
63	instantiation	77, 78, 79	⊢
	: , : , :
64	instantiation	81, 80	,  ⊢
	:
65	theorem		⊢
	proveit.numbers.division.mult_frac_left
66	instantiation	81, 82	,  ⊢
	:
67	theorem		⊢
	proveit.numbers.division.div_complex_closure
68	instantiation	123, 107, 83	⊢
	: , :
69	instantiation	84, 85	⊢
	: , :
70	instantiation	123, 107, 86	,  ⊢
	: , :
71	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
72	instantiation	87, 143, 98, 99, 142, 88	⊢
	: , : , : , : , :
73	instantiation	89, 98, 146, 143, 99, 90, 125, 107, 91	⊢
	: , : , : , : , : , :
74	instantiation	92, 107, 125, 93	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
76	instantiation	144, 94, 95	⊢
	: , : , :
77	axiom		⊢
	proveit.logic.equality.equals_transitivity
78	instantiation	96, 143, 98, 99, 107, 125	⊢
	: , : , : , : , : , : , :
79	instantiation	97, 98, 146, 143, 99, 100, 107, 125, 101*	⊢
	: , : , : , : , : , :
80	instantiation	123, 107, 102	,  ⊢
	: , :
81	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
82	instantiation	123, 112, 103	,  ⊢
	: , :
83	instantiation	113, 119	⊢
	:
84	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
85	instantiation	104, 105	⊢
	: , :
86	instantiation	113, 106	,  ⊢
	:
87	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
88	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
89	theorem		⊢
	proveit.numbers.addition.disassociation
90	instantiation	111	⊢
	: , :
91	instantiation	113, 107	⊢
	:
92	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
93	instantiation	108	⊢
	:
94	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
95	instantiation	144, 109, 110	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.addition.leftward_commutation
97	theorem		⊢
	proveit.numbers.addition.association
98	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
99	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
100	instantiation	111	⊢
	: , :
101	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
102	instantiation	113, 112	,  ⊢
	:
103	instantiation	113, 114	,  ⊢
	:
104	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
105	assumption		⊢
106	instantiation	118, 119, 115	,  ⊢
	: , :
107	instantiation	144, 128, 116	⊢
	: , : , :
108	axiom		⊢
	proveit.logic.equality.equals_reflexivity
109	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
110	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
111	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
112	instantiation	118, 119, 117	,  ⊢
	: , :
113	theorem		⊢
	proveit.numbers.negation.complex_closure
114	instantiation	118, 119, 120	,  ⊢
	: , :
115	instantiation	123, 125, 124	⊢
	: , :
116	instantiation	144, 131, 121	⊢
	: , : , :
117	instantiation	144, 128, 122	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
119	assumption		⊢
120	instantiation	123, 124, 125	⊢
	: , :
121	instantiation	144, 138, 137	⊢
	: , : , :
122	instantiation	144, 131, 126	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
124	instantiation	144, 128, 127	⊢
	: , : , :
125	instantiation	144, 128, 129	⊢
	: , : , :
126	instantiation	144, 138, 130	⊢
	: , : , :
127	instantiation	144, 131, 132	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
129	instantiation	133, 134, 142	⊢
	: , : , :
130	instantiation	135, 136, 137	⊢
	: , :
131	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
132	instantiation	144, 138, 139	⊢
	: , : , :
133	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
134	instantiation	140, 141	⊢
	: , :
135	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
136	instantiation	144, 145, 142	⊢
	: , : , :
137	instantiation	144, 145, 143	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
139	instantiation	144, 145, 146	⊢
	: , : , :
140	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
141	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_within_real
142	assumption		⊢
143	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
144	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
145	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
146	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements