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
2	instantiation	83, 75	⊢
	:
3	instantiation	7, 8, 9	⊢
	: , :
4	instantiation	11, 10	⊢
	: , :
5	instantiation	11, 12	⊢
	: , :
6	instantiation	42, 45, 80, 82, 47, 13, 14, 15, 56	,  ⊢
	: , : , : , : , : , :
7	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
8	instantiation	85, 16, 17	⊢
	: , : , :
9	instantiation	18, 19	⊢
	:
10	instantiation	31, 20, 21	⊢
	: , : , :
11	theorem		⊢
	proveit.logic.equality.equals_reversal
12	instantiation	31, 22, 23	⊢
	: , : , :
13	instantiation	58	⊢
	: , :
14	instantiation	85, 63, 24	,  ⊢
	: , : , :
15	instantiation	25, 53	⊢
	:
16	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
17	instantiation	26, 82, 45, 47, 27	⊢
	: , : , : , : , :
18	theorem		⊢
	proveit.numbers.negation.nat_closure
19	instantiation	28, 29, 30	⊢
	:
20	instantiation	34, 35	⊢
	: , : , :
21	instantiation	31, 32, 33	⊢
	: , : , :
22	instantiation	34, 35	⊢
	: , : , :
23	instantiation	36, 53	⊢
	:
24	instantiation	85, 69, 37	,  ⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.negation.complex_closure
26	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
27	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
28	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
29	instantiation	73, 77, 75	⊢
	: , :
30	instantiation	38, 62, 61, 64, 39, 40*, 41*	⊢
	: , : , :
31	axiom		⊢
	proveit.logic.equality.equals_transitivity
32	instantiation	42, 45, 80, 82, 47, 43, 54, 53	⊢
	: , : , : , : , : , :
33	instantiation	44, 82, 80, 45, 46, 47, 54, 53, 48*	⊢
	: , : , : , : , : , :
34	axiom		⊢
	proveit.logic.equality.substitution
35	instantiation	49, 53	⊢
	:
36	theorem		⊢
	proveit.numbers.addition.elim_zero_left
37	instantiation	85, 76, 50	,  ⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
39	instantiation	51, 87	⊢
	:
40	instantiation	52, 53, 54	⊢
	: , :
41	instantiation	55, 56, 57	⊢
	: , :
42	theorem		⊢
	proveit.numbers.addition.disassociation
43	instantiation	58	⊢
	: , :
44	theorem		⊢
	proveit.numbers.addition.association
45	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
46	instantiation	58	⊢
	: , :
47	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
48	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
49	theorem		⊢
	proveit.numbers.negation.double_negation
50	instantiation	85, 59, 60	,  ⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
52	theorem		⊢
	proveit.numbers.addition.commutation
53	instantiation	85, 63, 61	⊢
	: , : , :
54	instantiation	85, 63, 62	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
56	instantiation	85, 63, 64	⊢
	: , : , :
57	instantiation	65	⊢
	:
58	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
59	instantiation	66, 67, 75	⊢
	: , :
60	assumption		⊢
61	instantiation	85, 69, 68	⊢
	: , : , :
62	instantiation	85, 69, 70	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
64	instantiation	71, 72, 87	⊢
	: , : , :
65	axiom		⊢
	proveit.logic.equality.equals_reflexivity
66	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
67	instantiation	73, 77, 74	⊢
	: , :
68	instantiation	85, 76, 75	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
70	instantiation	85, 76, 77	⊢
	: , : , :
71	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
72	instantiation	78, 79	⊢
	: , :
73	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
74	instantiation	85, 81, 80	⊢
	: , : , :
75	instantiation	85, 81, 82	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
77	instantiation	83, 84	⊢
	:
78	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
79	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
81	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
82	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
83	theorem		⊢
	proveit.numbers.negation.int_closure
84	instantiation	85, 86, 87	⊢
	: , : , :
85	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
86	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
87	assumption		⊢
*equality replacement requirements