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	41	⊢
2	instantiation	77, 3, 4	⊢
	: , : , :
3	instantiation	5, 81, 6, 7, 8	⊢
	: , : , : , : , : , :
4	modus ponens	9, 10	⊢
5	theorem		⊢
	proveit.core_expr_types.tuples.shift_equivalence
6	instantiation	11, 12, 13	⊢
	:
7	instantiation	74, 14	⊢
	: , :
8	instantiation	74, 15	⊢
	: , :
9	instantiation	16, 134, 132	⊢
	: , : , : , : , :
10	generalization	17	⊢
11	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
12	instantiation	127, 18, 19	⊢
	: , :
13	instantiation	20, 21	⊢
	: , :
14	instantiation	77, 22, 23	⊢
	: , : , :
15	instantiation	60, 98, 24, 108, 25	⊢
	: , : , :
16	theorem		⊢
	proveit.core_expr_types.tuples.range_fn_transformation
17	instantiation	77, 26, 27	,  ⊢
	: , : , :
18	instantiation	137, 135, 28	⊢
	: , : , :
19	instantiation	133, 68	⊢
	:
20	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
21	instantiation	29, 30, 31, 106, 32, 33*, 34*	⊢
	: , : , :
22	instantiation	41, 35	⊢
	: , : , :
23	instantiation	77, 36, 37	⊢
	: , : , :
24	instantiation	137, 115, 38	⊢
	: , : , :
25	instantiation	77, 39, 40	⊢
	: , : , :
26	instantiation	41, 42	,  ⊢
	: , : , :
27	instantiation	77, 43, 44	,  ⊢
	: , : , :
28	instantiation	45, 46	⊢
	: , :
29	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
30	instantiation	137, 123, 47	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
32	instantiation	48, 49	⊢
	: , :
33	instantiation	77, 50, 51	⊢
	: , : , :
34	instantiation	52, 53, 54, 55	⊢
	: , : , : , :
35	instantiation	56, 96, 108, 57*	⊢
	: , :
36	instantiation	77, 58, 59	⊢
	: , : , :
37	instantiation	60, 108, 97, 75	⊢
	: , : , :
38	instantiation	137, 123, 61	⊢
	: , : , :
39	instantiation	91, 139, 129, 92, 62, 95, 98, 96, 108	⊢
	: , : , : , : , : , :
40	instantiation	88, 98, 108, 89	⊢
	: , : , :
41	axiom		⊢
	proveit.logic.equality.substitution
42	instantiation	91, 139, 129, 92, 62, 95, 87, 96, 108	,  ⊢
	: , : , : , : , : , :
43	instantiation	91, 92, 63, 129, 95, 64, 65, 87, 96, 108, 99, 98	,  ⊢
	: , : , : , : , : , :
44	instantiation	77, 66, 67	,  ⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
47	instantiation	137, 130, 68	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.ordering.relax_less
49	instantiation	69, 136	⊢
	:
50	instantiation	91, 139, 129, 92, 93, 95, 70, 96, 97	⊢
	: , : , : , : , : , :
51	instantiation	71, 92, 129, 95, 93, 96, 97	⊢
	: , : , : , :
52	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
53	instantiation	77, 72, 73	⊢
	: , : , :
54	instantiation	101	⊢
	:
55	instantiation	74, 75	⊢
	: , :
56	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
57	instantiation	76, 98	⊢
	:
58	instantiation	77, 78, 79	⊢
	: , : , :
59	instantiation	80, 92, 139, 95, 98, 97, 99	⊢
	: , : , : , : , : , : , : , :
60	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
61	instantiation	137, 130, 81	⊢
	: , : , :
62	instantiation	103	⊢
	: , :
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
64	instantiation	82	⊢
	: , : , :
65	instantiation	103	⊢
	: , :
66	instantiation	83, 129, 92, 139, 84, 95, 87, 96, 108, 98, 85	,  ⊢
	: , : , : , : , : , : , : , :
67	instantiation	86, 98, 87, 89	,  ⊢
	: , : , :
68	instantiation	127, 119, 120	⊢
	: , :
69	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
70	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
71	theorem		⊢
	proveit.numbers.addition.elim_zero_any
72	instantiation	91, 139, 129, 92, 93, 95, 98, 96, 97	⊢
	: , : , : , : , : , :
73	instantiation	88, 98, 97, 89	⊢
	: , : , :
74	theorem		⊢
	proveit.logic.equality.equals_reversal
75	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
76	theorem		⊢
	proveit.numbers.negation.double_negation
77	axiom		⊢
	proveit.logic.equality.equals_transitivity
78	instantiation	91, 92, 129, 139, 95, 93, 96, 97, 90	⊢
	: , : , : , : , : , :
79	instantiation	91, 129, 92, 93, 94, 95, 96, 97, 98, 99	⊢
	: , : , : , : , : , :
80	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general_rev
81	instantiation	127, 119, 134	⊢
	: , :
82	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
83	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
84	instantiation	103	⊢
	: , :
85	instantiation	101	⊢
	:
86	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
87	instantiation	137, 115, 100	,  ⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
89	instantiation	101	⊢
	:
90	instantiation	137, 115, 102	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.addition.disassociation
92	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
93	instantiation	103	⊢
	: , :
94	instantiation	103	⊢
	: , :
95	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
96	instantiation	137, 115, 104	⊢
	: , : , :
97	instantiation	137, 115, 105	⊢
	: , : , :
98	instantiation	137, 115, 106	⊢
	: , : , :
99	instantiation	107, 108	⊢
	:
100	instantiation	137, 123, 109	,  ⊢
	: , : , :
101	axiom		⊢
	proveit.logic.equality.equals_reflexivity
102	instantiation	137, 123, 110	⊢
	: , : , :
103	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
104	instantiation	137, 123, 111	⊢
	: , : , :
105	instantiation	137, 123, 112	⊢
	: , : , :
106	instantiation	113, 114, 136	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.negation.complex_closure
108	instantiation	137, 115, 116	⊢
	: , : , :
109	instantiation	137, 130, 117	,  ⊢
	: , : , :
110	instantiation	137, 130, 118	⊢
	: , : , :
111	instantiation	137, 130, 119	⊢
	: , : , :
112	instantiation	137, 130, 120	⊢
	: , : , :
113	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
114	instantiation	121, 122	⊢
	: , :
115	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
116	instantiation	137, 123, 124	⊢
	: , : , :
117	instantiation	137, 125, 126	,  ⊢
	: , : , :
118	instantiation	127, 132, 128	⊢
	: , :
119	instantiation	133, 132	⊢
	:
120	instantiation	137, 138, 129	⊢
	: , : , :
121	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
122	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
123	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
124	instantiation	137, 130, 134	⊢
	: , : , :
125	instantiation	131, 134, 132	⊢
	: , :
126	assumption		⊢
127	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
128	instantiation	133, 134	⊢
	:
129	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
130	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
131	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
132	instantiation	137, 135, 136	⊢
	: , : , :
133	theorem		⊢
	proveit.numbers.negation.int_closure
134	instantiation	137, 138, 139	⊢
	: , : , :
135	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
136	assumption		⊢
137	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
138	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
139	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements