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	, ,  ⊢
	:
1	modus ponens	3, 4	,  ⊢
2	assumption		⊢
3	instantiation	5, 6*, 7*	,  ⊢
	:
4	instantiation	8, 9, 10	,  ⊢
	: , :
5	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.fold_forall_natural
6	instantiation	107, 11, 12	,  ⊢
	: , : , :
7	instantiation	107, 13, 14	⊢
	: , : , :
8	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
9	axiom		⊢
	proveit.logic.booleans.true_axiom
10	generalization	15	,  ⊢
11	instantiation	16, 177, 17, 131, 18, 19	,  ⊢
	: , : , : , :
12	instantiation	20, 124	⊢
	:
13	instantiation	120, 129, 177, 174, 130, 121, 156, 138	⊢
	: , : , : , : , : , :
14	instantiation	128, 174, 177, 129, 131, 130, 156, 138, 132*	⊢
	: , : , : , : , : , :
15	instantiation	107, 21, 22	, , ,  ⊢
	: , : , :
16	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
17	instantiation	142	⊢
	: , :
18	instantiation	23, 81, 24*	⊢
	: , :
19	instantiation	107, 25, 26	,  ⊢
	: , : , :
20	axiom		⊢
	proveit.logic.booleans.eq_true_intro
21	instantiation	58, 27, 28	, , ,  ⊢
	: , : , :
22	instantiation	69, 29	, ,  ⊢
	: , :
23	axiom		⊢
	proveit.numbers.summation.sum_single
24	instantiation	30, 150	⊢
	:
25	instantiation	98, 31	⊢
	: , : , :
26	instantiation	32, 95, 96	,  ⊢
	:
27	instantiation	58, 33, 34	, , ,  ⊢
	: , : , :
28	instantiation	51, 35, 36, 37, 38*	, ,  ⊢
	: , : , : , :
29	instantiation	58, 39, 40	, ,  ⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
31	instantiation	98, 41	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
33	instantiation	42, 43, 44	, , ,  ⊢
	: , : , :
34	instantiation	45, 129, 174, 130, 138, 150, 143, 46*, 47*	,  ⊢
	: , : , : , : , : , :
35	instantiation	98, 48	, ,  ⊢
	: , : , :
36	instantiation	98, 49	, ,  ⊢
	: , : , :
37	instantiation	69, 50	, ,  ⊢
	: , :
38	instantiation	51, 52, 53, 54	,  ⊢
	: , : , : , :
39	instantiation	69, 55	, ,  ⊢
	: , :
40	instantiation	56, 156, 155	⊢
	: , :
41	instantiation	98, 57	⊢
	: , : , :
42	theorem		⊢
	proveit.logic.equality.sub_left_side_into
43	instantiation	58, 59, 60	,  ⊢
	: , : , :
44	instantiation	61, 62, 63, 143, 64*, 65*	, ,  ⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.multiplication.distribute_through_subtract
46	instantiation	111, 143	,  ⊢
	:
47	instantiation	66, 150, 141, 102, 79*, 67*	,  ⊢
	: , : , :
48	instantiation	69, 68	, ,  ⊢
	: , :
49	instantiation	69, 70	, ,  ⊢
	: , :
50	instantiation	71, 174, 177, 129, 72, 130, 73, 110, 112	, ,  ⊢
	: , : , : , : , : , :
51	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
52	instantiation	120, 129, 177, 174, 130, 74, 138, 133, 112	,  ⊢
	: , : , : , : , : , :
53	instantiation	120, 177, 129, 74, 75, 130, 138, 133, 143, 134	,  ⊢
	: , : , : , : , : , :
54	instantiation	76, 174, 129, 130, 138, 143, 134	,  ⊢
	: , : , : , : , : , : , : , :
55	instantiation	92, 138, 97, 95, 96, 77*	, ,  ⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.addition.commutation
57	instantiation	107, 78, 79	⊢
	: , : , :
58	theorem		⊢
	proveit.logic.equality.sub_right_side_into
59	instantiation	80, 81, 161, 82, 83*	⊢
	: , : , : , :
60	assumption		⊢
61	theorem		⊢
	proveit.numbers.division.frac_cancel_left
62	instantiation	84, 95, 96	,  ⊢
	:
63	instantiation	175, 85, 86	⊢
	: , : , :
64	instantiation	87, 95	⊢
	:
65	instantiation	88, 143	,  ⊢
	:
66	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
67	instantiation	107, 89, 90	⊢
	: , : , :
68	instantiation	92, 138, 110, 95, 96, 91*	, ,  ⊢
	: , : , :
69	theorem		⊢
	proveit.logic.equality.equals_reversal
70	instantiation	92, 138, 112, 95, 96, 93*	, ,  ⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
72	instantiation	142	⊢
	: , :
73	instantiation	94, 138, 95, 96	,  ⊢
	: , :
74	instantiation	142	⊢
	: , :
75	instantiation	142	⊢
	: , :
76	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general_rev
77	instantiation	111, 97	,  ⊢
	:
78	instantiation	98, 99	⊢
	: , : , :
79	instantiation	100, 150	⊢
	:
80	axiom		⊢
	proveit.numbers.summation.sum_split_last
81	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
82	instantiation	101, 102	⊢
	:
83	instantiation	107, 103, 104	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
85	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
86	instantiation	175, 105, 106	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
88	theorem		⊢
	proveit.numbers.division.frac_one_denom
89	instantiation	120, 174, 177, 129, 121, 130, 138, 156	⊢
	: , : , : , : , : , :
90	instantiation	107, 108, 109	⊢
	: , : , :
91	instantiation	111, 110	,  ⊢
	:
92	theorem		⊢
	proveit.numbers.division.mult_frac_left
93	instantiation	111, 112	,  ⊢
	:
94	theorem		⊢
	proveit.numbers.division.div_complex_closure
95	instantiation	154, 138, 113	⊢
	: , :
96	instantiation	114, 115	⊢
	: , :
97	instantiation	154, 138, 116	,  ⊢
	: , :
98	axiom		⊢
	proveit.logic.equality.substitution
99	instantiation	117, 138	⊢
	:
100	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
101	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
102	instantiation	118, 174, 129, 130, 173, 119	⊢
	: , : , : , : , :
103	instantiation	120, 129, 177, 174, 130, 121, 156, 138, 122	⊢
	: , : , : , : , : , :
104	instantiation	123, 138, 156, 124	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
106	instantiation	175, 125, 126	⊢
	: , : , :
107	axiom		⊢
	proveit.logic.equality.equals_transitivity
108	instantiation	127, 174, 129, 130, 138, 156	⊢
	: , : , : , : , : , : , :
109	instantiation	128, 129, 177, 174, 130, 131, 138, 156, 132*	⊢
	: , : , : , : , : , :
110	instantiation	154, 138, 133	,  ⊢
	: , :
111	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
112	instantiation	154, 143, 134	,  ⊢
	: , :
113	instantiation	144, 150	⊢
	:
114	theorem		⊢
	proveit.numbers.addition.subtraction.nonzero_difference_if_different
115	instantiation	135, 136	⊢
	: , :
116	instantiation	144, 137	,  ⊢
	:
117	theorem		⊢
	proveit.numbers.addition.elim_zero_left
118	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
119	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
120	theorem		⊢
	proveit.numbers.addition.disassociation
121	instantiation	142	⊢
	: , :
122	instantiation	144, 138	⊢
	:
123	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
124	instantiation	139	⊢
	:
125	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
126	instantiation	175, 140, 141	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.addition.leftward_commutation
128	theorem		⊢
	proveit.numbers.addition.association
129	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
130	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
131	instantiation	142	⊢
	: , :
132	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
133	instantiation	144, 143	,  ⊢
	:
134	instantiation	144, 145	,  ⊢
	:
135	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
136	assumption		⊢
137	instantiation	149, 150, 146	,  ⊢
	: , :
138	instantiation	175, 159, 147	⊢
	: , : , :
139	axiom		⊢
	proveit.logic.equality.equals_reflexivity
140	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
141	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
142	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
143	instantiation	149, 150, 148	,  ⊢
	: , :
144	theorem		⊢
	proveit.numbers.negation.complex_closure
145	instantiation	149, 150, 151	,  ⊢
	: , :
146	instantiation	154, 156, 155	⊢
	: , :
147	instantiation	175, 162, 152	⊢
	: , : , :
148	instantiation	175, 159, 153	⊢
	: , : , :
149	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
150	assumption		⊢
151	instantiation	154, 155, 156	⊢
	: , :
152	instantiation	175, 169, 168	⊢
	: , : , :
153	instantiation	175, 162, 157	⊢
	: , : , :
154	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
155	instantiation	175, 159, 158	⊢
	: , : , :
156	instantiation	175, 159, 160	⊢
	: , : , :
157	instantiation	175, 169, 161	⊢
	: , : , :
158	instantiation	175, 162, 163	⊢
	: , : , :
159	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
160	instantiation	164, 165, 173	⊢
	: , : , :
161	instantiation	166, 167, 168	⊢
	: , :
162	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
163	instantiation	175, 169, 170	⊢
	: , : , :
164	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
165	instantiation	171, 172	⊢
	: , :
166	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
167	instantiation	175, 176, 173	⊢
	: , : , :
168	instantiation	175, 176, 174	⊢
	: , : , :
169	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
170	instantiation	175, 176, 177	⊢
	: , : , :
171	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
172	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_within_real
173	assumption		⊢
174	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
175	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
176	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
177	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements