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, 4, 5	⊢
	: , : , : , :
1	theorem		⊢
	proveit.core_expr_types.operations.operands_substitution_via_tuple
2	reference	40	⊢
3	instantiation	93, 6	⊢
	: , : , :
4	instantiation	95, 7, 92, 8	⊢
	: , : , : , :
5	instantiation	9, 10, 11, 44*	⊢
	: , : , :
6	instantiation	12, 132, 13, 14, 15, 16*	⊢
	: , : , : , : , : , :
7	instantiation	17, 18, 19, 20, 21, 22, 23, 24*	⊢
	: , : , : , :
8	instantiation	71, 25	⊢
	: , :
9	theorem		⊢
	proveit.core_expr_types.tuples.partition_front
10	instantiation	28, 112, 35	⊢
	: , :
11	instantiation	86, 26, 27	⊢
	: , : , :
12	theorem		⊢
	proveit.core_expr_types.tuples.shift_equivalence
13	instantiation	28, 29, 35	⊢
	: , :
14	instantiation	71, 30	⊢
	: , :
15	instantiation	71, 31	⊢
	: , :
16	instantiation	86, 32, 33	,  ⊢
	: , : , :
17	theorem		⊢
	proveit.core_expr_types.tuples.general_len
18	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
19	instantiation	121	⊢
	: , :
20	instantiation	121	⊢
	: , :
21	instantiation	121	⊢
	: , :
22	instantiation	34, 150, 58	⊢
	: , : , :
23	instantiation	122, 35, 36	⊢
	: , : , :
24	instantiation	86, 37, 38	⊢
	: , : , :
25	instantiation	39, 40	⊢
	: , :
26	instantiation	105, 112, 155, 150, 114, 78, 103, 130	⊢
	: , : , : , : , : , :
27	instantiation	111, 150, 155, 112, 41, 114, 103, 130, 128*	⊢
	: , : , : , : , : , :
28	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
29	instantiation	153, 61, 42	⊢
	: , : , :
30	instantiation	86, 43, 44	⊢
	: , : , :
31	instantiation	86, 45, 46	⊢
	: , : , :
32	instantiation	105, 112, 155, 150, 114, 47, 49, 103, 119	,  ⊢
	: , : , : , : , : , :
33	instantiation	48, 119, 49, 92	,  ⊢
	: , : , :
34	theorem		⊢
	proveit.logic.equality.sub_left_side_into
35	instantiation	50, 51	⊢
	:
36	instantiation	95, 52, 53, 54	⊢
	: , : , : , :
37	instantiation	55, 155, 56, 57, 58, 72	⊢
	: , : , : , :
38	instantiation	86, 59, 60	⊢
	: , : , :
39	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
40	instantiation	153, 61, 146	⊢
	: , : , :
41	instantiation	121	⊢
	: , :
42	instantiation	62, 150, 112, 114, 63	⊢
	: , : , : , : , :
43	instantiation	93, 104	⊢
	: , : , :
44	instantiation	86, 64, 65	⊢
	: , : , :
45	instantiation	93, 104	⊢
	: , : , :
46	instantiation	66, 119	⊢
	:
47	instantiation	121	⊢
	: , :
48	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
49	instantiation	153, 143, 67	,  ⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.negation.nat_closure
51	instantiation	68, 69, 70	⊢
	:
52	instantiation	102, 103, 130, 104*	⊢
	: , :
53	instantiation	101	⊢
	:
54	instantiation	71, 72	⊢
	: , :
55	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
56	instantiation	121	⊢
	: , :
57	instantiation	121	⊢
	: , :
58	instantiation	73, 130, 77	⊢
	: , : , :
59	instantiation	105, 150, 155, 112, 74, 114, 130, 119, 75	⊢
	: , : , : , : , : , :
60	instantiation	76, 130, 119, 77	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
62	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
63	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
64	instantiation	105, 112, 155, 150, 114, 78, 103, 130, 119	⊢
	: , : , : , : , : , :
65	instantiation	79, 119, 130, 92	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.addition.elim_zero_left
67	instantiation	153, 148, 80	,  ⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
69	instantiation	81, 132, 147	⊢
	: , :
70	instantiation	82, 117, 135, 126, 83, 84*, 85*	⊢
	: , : , :
71	theorem		⊢
	proveit.logic.equality.equals_reversal
72	instantiation	86, 87, 88	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
74	instantiation	121	⊢
	: , :
75	instantiation	136, 130	⊢
	:
76	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
77	instantiation	101	⊢
	:
78	instantiation	121	⊢
	: , :
79	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_31
80	instantiation	153, 151, 89	,  ⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
82	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
83	instantiation	90, 146	⊢
	:
84	instantiation	129, 130, 103	⊢
	: , :
85	instantiation	91, 119, 92	⊢
	: , :
86	axiom		⊢
	proveit.logic.equality.equals_transitivity
87	instantiation	93, 94	⊢
	: , : , :
88	instantiation	95, 96, 97, 98	⊢
	: , : , : , :
89	instantiation	153, 99, 100	,  ⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
91	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
92	instantiation	101	⊢
	:
93	axiom		⊢
	proveit.logic.equality.substitution
94	instantiation	102, 103, 137, 104*	⊢
	: , :
95	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
96	instantiation	105, 150, 155, 106, 107, 119, 131, 130	⊢
	: , : , : , : , : , :
97	instantiation	108, 112, 109, 114, 110, 119, 131, 130	⊢
	: , : , : , :
98	instantiation	111, 150, 155, 112, 113, 114, 119, 131, 130, 115*	⊢
	: , : , : , : , : , :
99	instantiation	116, 147, 139	⊢
	: , :
100	assumption		⊢
101	axiom		⊢
	proveit.logic.equality.equals_reflexivity
102	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
103	instantiation	153, 143, 117	⊢
	: , : , :
104	instantiation	118, 119	⊢
	:
105	theorem		⊢
	proveit.numbers.addition.disassociation
106	instantiation	121	⊢
	: , :
107	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
108	theorem		⊢
	proveit.numbers.addition.elim_zero_any
109	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
110	instantiation	120	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.addition.association
112	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
113	instantiation	121	⊢
	: , :
114	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
115	instantiation	122, 123, 124	⊢
	: , : , :
116	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
117	instantiation	153, 148, 125	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.negation.double_negation
119	instantiation	153, 143, 126	⊢
	: , : , :
120	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
121	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
122	theorem		⊢
	proveit.logic.equality.sub_right_side_into
123	instantiation	127, 130, 137, 128	⊢
	: , : , :
124	instantiation	129, 130, 131	⊢
	: , :
125	instantiation	153, 151, 132	⊢
	: , : , :
126	instantiation	133, 134, 146	⊢
	: , : , :
127	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
128	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
129	theorem		⊢
	proveit.numbers.addition.commutation
130	instantiation	153, 143, 135	⊢
	: , : , :
131	instantiation	136, 137	⊢
	:
132	instantiation	138, 139	⊢
	:
133	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
134	instantiation	140, 141	⊢
	: , :
135	instantiation	153, 148, 142	⊢
	: , : , :
136	theorem		⊢
	proveit.numbers.negation.complex_closure
137	instantiation	153, 143, 144	⊢
	: , : , :
138	theorem		⊢
	proveit.numbers.negation.int_closure
139	instantiation	153, 145, 146	⊢
	: , : , :
140	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
141	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
142	instantiation	153, 151, 147	⊢
	: , : , :
143	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
144	instantiation	153, 148, 149	⊢
	: , : , :
145	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
146	assumption		⊢
147	instantiation	153, 154, 150	⊢
	: , : , :
148	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
149	instantiation	153, 151, 152	⊢
	: , : , :
150	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
151	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
152	instantiation	153, 154, 155	⊢
	: , : , :
153	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
154	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
155	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements