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