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	reference	72	⊢
2	instantiation	3, 41, 4, 5, 6	⊢
	: , : , : , :
3	theorem		⊢
	proveit.core_expr_types.operations.operands_substitution_via_tuple
4	instantiation	94, 7	⊢
	: , : , :
5	instantiation	96, 8, 93, 9	⊢
	: , : , : , :
6	instantiation	10, 11, 12, 45*	⊢
	: , : , :
7	instantiation	13, 133, 14, 15, 16, 17*	⊢
	: , : , : , : , : , :
8	instantiation	18, 19, 20, 21, 22, 23, 24, 25*	⊢
	: , : , : , :
9	instantiation	72, 26	⊢
	: , :
10	theorem		⊢
	proveit.core_expr_types.tuples.partition_front
11	instantiation	29, 113, 36	⊢
	: , :
12	instantiation	87, 27, 28	⊢
	: , : , :
13	theorem		⊢
	proveit.core_expr_types.tuples.shift_equivalence
14	instantiation	29, 30, 36	⊢
	: , :
15	instantiation	72, 31	⊢
	: , :
16	instantiation	72, 32	⊢
	: , :
17	instantiation	87, 33, 34	,  ⊢
	: , : , :
18	theorem		⊢
	proveit.core_expr_types.tuples.general_len
19	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
20	instantiation	122	⊢
	: , :
21	instantiation	122	⊢
	: , :
22	instantiation	122	⊢
	: , :
23	instantiation	35, 151, 59	⊢
	: , : , :
24	instantiation	123, 36, 37	⊢
	: , : , :
25	instantiation	87, 38, 39	⊢
	: , : , :
26	instantiation	40, 41	⊢
	: , :
27	instantiation	106, 113, 156, 151, 115, 79, 104, 131	⊢
	: , : , : , : , : , :
28	instantiation	112, 151, 156, 113, 42, 115, 104, 131, 129*	⊢
	: , : , : , : , : , :
29	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
30	instantiation	154, 62, 43	⊢
	: , : , :
31	instantiation	87, 44, 45	⊢
	: , : , :
32	instantiation	87, 46, 47	⊢
	: , : , :
33	instantiation	106, 113, 156, 151, 115, 48, 50, 104, 120	,  ⊢
	: , : , : , : , : , :
34	instantiation	49, 120, 50, 93	,  ⊢
	: , : , :
35	theorem		⊢
	proveit.logic.equality.sub_left_side_into
36	instantiation	51, 52	⊢
	:
37	instantiation	96, 53, 54, 55	⊢
	: , : , : , :
38	instantiation	56, 156, 57, 58, 59, 73	⊢
	: , : , : , :
39	instantiation	87, 60, 61	⊢
	: , : , :
40	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
41	instantiation	154, 62, 147	⊢
	: , : , :
42	instantiation	122	⊢
	: , :
43	instantiation	63, 151, 113, 115, 64	⊢
	: , : , : , : , :
44	instantiation	94, 105	⊢
	: , : , :
45	instantiation	87, 65, 66	⊢
	: , : , :
46	instantiation	94, 105	⊢
	: , : , :
47	instantiation	67, 120	⊢
	:
48	instantiation	122	⊢
	: , :
49	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
50	instantiation	154, 144, 68	,  ⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.negation.nat_closure
52	instantiation	69, 70, 71	⊢
	:
53	instantiation	103, 104, 131, 105*	⊢
	: , :
54	instantiation	102	⊢
	:
55	instantiation	72, 73	⊢
	: , :
56	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
57	instantiation	122	⊢
	: , :
58	instantiation	122	⊢
	: , :
59	instantiation	74, 131, 78	⊢
	: , : , :
60	instantiation	106, 151, 156, 113, 75, 115, 131, 120, 76	⊢
	: , : , : , : , : , :
61	instantiation	77, 131, 120, 78	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
63	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
64	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
65	instantiation	106, 113, 156, 151, 115, 79, 104, 131, 120	⊢
	: , : , : , : , : , :
66	instantiation	80, 120, 131, 93	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.addition.elim_zero_left
68	instantiation	154, 149, 81	,  ⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
70	instantiation	82, 133, 148	⊢
	: , :
71	instantiation	83, 118, 136, 127, 84, 85*, 86*	⊢
	: , : , :
72	theorem		⊢
	proveit.logic.equality.equals_reversal
73	instantiation	87, 88, 89	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
75	instantiation	122	⊢
	: , :
76	instantiation	137, 131	⊢
	:
77	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
78	instantiation	102	⊢
	:
79	instantiation	122	⊢
	: , :
80	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_31
81	instantiation	154, 152, 90	,  ⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
83	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
84	instantiation	91, 147	⊢
	:
85	instantiation	130, 131, 104	⊢
	: , :
86	instantiation	92, 120, 93	⊢
	: , :
87	axiom		⊢
	proveit.logic.equality.equals_transitivity
88	instantiation	94, 95	⊢
	: , : , :
89	instantiation	96, 97, 98, 99	⊢
	: , : , : , :
90	instantiation	154, 100, 101	,  ⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
92	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
93	instantiation	102	⊢
	:
94	axiom		⊢
	proveit.logic.equality.substitution
95	instantiation	103, 104, 138, 105*	⊢
	: , :
96	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
97	instantiation	106, 151, 156, 107, 108, 120, 132, 131	⊢
	: , : , : , : , : , :
98	instantiation	109, 113, 110, 115, 111, 120, 132, 131	⊢
	: , : , : , :
99	instantiation	112, 151, 156, 113, 114, 115, 120, 132, 131, 116*	⊢
	: , : , : , : , : , :
100	instantiation	117, 148, 140	⊢
	: , :
101	assumption		⊢
102	axiom		⊢
	proveit.logic.equality.equals_reflexivity
103	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
104	instantiation	154, 144, 118	⊢
	: , : , :
105	instantiation	119, 120	⊢
	:
106	theorem		⊢
	proveit.numbers.addition.disassociation
107	instantiation	122	⊢
	: , :
108	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
109	theorem		⊢
	proveit.numbers.addition.elim_zero_any
110	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
111	instantiation	121	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.addition.association
113	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
114	instantiation	122	⊢
	: , :
115	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
116	instantiation	123, 124, 125	⊢
	: , : , :
117	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
118	instantiation	154, 149, 126	⊢
	: , : , :
119	theorem		⊢
	proveit.numbers.negation.double_negation
120	instantiation	154, 144, 127	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
122	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
123	theorem		⊢
	proveit.logic.equality.sub_right_side_into
124	instantiation	128, 131, 138, 129	⊢
	: , : , :
125	instantiation	130, 131, 132	⊢
	: , :
126	instantiation	154, 152, 133	⊢
	: , : , :
127	instantiation	134, 135, 147	⊢
	: , : , :
128	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
129	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
130	theorem		⊢
	proveit.numbers.addition.commutation
131	instantiation	154, 144, 136	⊢
	: , : , :
132	instantiation	137, 138	⊢
	:
133	instantiation	139, 140	⊢
	:
134	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
135	instantiation	141, 142	⊢
	: , :
136	instantiation	154, 149, 143	⊢
	: , : , :
137	theorem		⊢
	proveit.numbers.negation.complex_closure
138	instantiation	154, 144, 145	⊢
	: , : , :
139	theorem		⊢
	proveit.numbers.negation.int_closure
140	instantiation	154, 146, 147	⊢
	: , : , :
141	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
142	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
143	instantiation	154, 152, 148	⊢
	: , : , :
144	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
145	instantiation	154, 149, 150	⊢
	: , : , :
146	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
147	assumption		⊢
148	instantiation	154, 155, 151	⊢
	: , : , :
149	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
150	instantiation	154, 152, 153	⊢
	: , : , :
151	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
152	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
153	instantiation	154, 155, 156	⊢
	: , : , :
154	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
155	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
156	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements