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