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, 6	, ,  ⊢
	: , : , : , : , : , : , :
1	theorem		⊢
	proveit.core_expr_types.tuples.shift_equivalence_both
2	reference	117	⊢
3	reference	91	⊢
4	instantiation	7, 8, 9	, ,  ⊢
	:
5	instantiation	56, 10, 89, 11	⊢
	: , : , : , :
6	instantiation	56, 53, 40, 12	⊢
	: , : , : , :
7	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
8	instantiation	111, 13, 14	,  ⊢
	: , :
9	instantiation	15, 16	, ,  ⊢
	: , :
10	instantiation	69, 17, 18	⊢
	: , : , :
11	instantiation	52, 19	⊢
	: , :
12	instantiation	52, 20	⊢
	: , :
13	instantiation	111, 21, 117	⊢
	: , :
14	instantiation	22, 104	⊢
	:
15	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
16	instantiation	23, 79, 24, 25, 26, 27*, 28*	, ,  ⊢
	: , : , :
17	instantiation	77, 82, 102, 124, 84, 68, 97, 73, 93	⊢
	: , : , : , : , : , :
18	instantiation	87, 93, 97, 86	⊢
	: , : , :
19	instantiation	69, 29, 30	⊢
	: , : , :
20	instantiation	69, 31, 32	⊢
	: , : , :
21	instantiation	111, 115, 112	⊢
	: , :
22	theorem		⊢
	proveit.numbers.negation.int_closure
23	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
25	instantiation	33, 34, 36	⊢
	: , : , :
26	instantiation	35, 36	⊢
	:
27	instantiation	69, 37, 38	⊢
	: , : , :
28	instantiation	56, 39, 40, 41	,  ⊢
	: , : , : , :
29	instantiation	77, 82, 102, 124, 84, 42, 97, 44, 54	⊢
	: , : , : , : , : , :
30	instantiation	87, 54, 97, 45	⊢
	: , : , :
31	instantiation	77, 82, 102, 124, 84, 43, 88, 44, 54	⊢
	: , : , : , : , : , :
32	instantiation	87, 54, 88, 45	⊢
	: , : , :
33	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
34	instantiation	46, 47	⊢
	: , :
35	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
36	assumption		⊢
37	instantiation	77, 124, 102, 82, 68, 84, 48, 97, 73	⊢
	: , : , : , : , : , :
38	instantiation	49, 82, 102, 84, 68, 97, 73	⊢
	: , : , : , :
39	instantiation	69, 50, 51	,  ⊢
	: , : , :
40	instantiation	99	⊢
	:
41	instantiation	52, 53	⊢
	: , :
42	instantiation	95	⊢
	: , :
43	instantiation	95	⊢
	: , :
44	instantiation	96, 54	⊢
	:
45	instantiation	99	⊢
	:
46	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_within_real
48	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
49	theorem		⊢
	proveit.numbers.addition.elim_zero_any
50	instantiation	75, 55	,  ⊢
	: , : , :
51	instantiation	56, 57, 58, 59	,  ⊢
	: , : , : , :
52	theorem		⊢
	proveit.logic.equality.equals_reversal
53	instantiation	69, 60, 61	⊢
	: , : , :
54	instantiation	122, 105, 62	⊢
	: , : , :
55	instantiation	69, 63, 64	,  ⊢
	: , : , :
56	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
57	instantiation	77, 82, 66, 124, 84, 67, 88, 85, 93, 65	,  ⊢
	: , : , : , : , : , :
58	instantiation	77, 66, 102, 82, 67, 68, 84, 88, 85, 93, 97, 73	,  ⊢
	: , : , : , : , : , :
59	instantiation	69, 70, 71	,  ⊢
	: , : , :
60	instantiation	77, 82, 102, 124, 84, 72, 88, 73, 93	⊢
	: , : , : , : , : , :
61	instantiation	87, 93, 88, 86	⊢
	: , : , :
62	instantiation	122, 113, 74	⊢
	: , : , :
63	instantiation	75, 76	⊢
	: , : , :
64	instantiation	77, 124, 102, 82, 78, 84, 88, 85, 93	,  ⊢
	: , : , : , : , : , :
65	instantiation	122, 105, 79	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
67	instantiation	80	⊢
	: , : , :
68	instantiation	95	⊢
	: , :
69	axiom		⊢
	proveit.logic.equality.equals_transitivity
70	instantiation	81, 102, 124, 82, 83, 84, 88, 85, 93, 97, 86	,  ⊢
	: , : , : , : , : , : , : , :
71	instantiation	87, 97, 88, 89	,  ⊢
	: , : , :
72	instantiation	95	⊢
	: , :
73	instantiation	122, 105, 90	⊢
	: , : , :
74	instantiation	122, 120, 91	⊢
	: , : , :
75	axiom		⊢
	proveit.logic.equality.substitution
76	instantiation	92, 97, 93	⊢
	: , :
77	theorem		⊢
	proveit.numbers.addition.disassociation
78	instantiation	95	⊢
	: , :
79	instantiation	122, 113, 94	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
81	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
82	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
83	instantiation	95	⊢
	: , :
84	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
85	instantiation	96, 97	⊢
	:
86	instantiation	99	⊢
	:
87	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
88	instantiation	122, 105, 98	⊢
	: , : , :
89	instantiation	99	⊢
	:
90	instantiation	122, 100, 101	⊢
	: , : , :
91	instantiation	122, 123, 102	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_subtract
93	instantiation	122, 105, 103	⊢
	: , : , :
94	instantiation	122, 120, 104	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
96	theorem		⊢
	proveit.numbers.negation.complex_closure
97	instantiation	122, 105, 106	⊢
	: , : , :
98	instantiation	122, 113, 107	⊢
	: , : , :
99	axiom		⊢
	proveit.logic.equality.equals_reflexivity
100	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
101	instantiation	122, 108, 109	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
103	instantiation	122, 113, 110	⊢
	: , : , :
104	instantiation	111, 121, 112	⊢
	: , :
105	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
106	instantiation	122, 113, 114	⊢
	: , : , :
107	instantiation	122, 120, 115	⊢
	: , : , :
108	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
109	instantiation	122, 116, 119	⊢
	: , : , :
110	instantiation	122, 120, 117	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
112	instantiation	122, 118, 119	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
114	instantiation	122, 120, 121	⊢
	: , : , :
115	assumption		⊢
116	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
117	instantiation	122, 123, 124	⊢
	: , : , :
118	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
119	instantiation	125, 126	⊢
	:
120	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
121	assumption		⊢
122	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
123	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
124	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
125	theorem		⊢
	proveit.numbers.negation.int_neg_closure
126	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
*equality replacement requirements