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, 7, 8*	⊢
	: , : , : , :
1	theorem		⊢
	proveit.core_expr_types.tuples.general_len
2	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
3	instantiation	69	⊢
	: , : , :
4	instantiation	69	⊢
	: , : , :
5	instantiation	69	⊢
	: , : , :
6	instantiation	9, 92, 20	⊢
	: , : , :
7	instantiation	10, 59, 11, 58, 12, 92	⊢
	: , :
8	instantiation	28, 13, 14	⊢
	: , : , :
9	theorem		⊢
	proveit.logic.equality.sub_left_side_into
10	theorem		⊢
	proveit.numbers.addition.add_nat_closure
11	instantiation	69	⊢
	: , : , :
12	instantiation	15, 16	⊢
	:
13	instantiation	17, 59, 18, 19, 20, 21	⊢
	: , : , : , :
14	instantiation	28, 22, 23	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.negation.nat_closure
16	instantiation	24, 25, 26	⊢
	:
17	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
18	instantiation	69	⊢
	: , : , :
19	instantiation	69	⊢
	: , : , :
20	instantiation	27, 71, 64	⊢
	: , : , :
21	instantiation	28, 29, 30	⊢
	: , : , :
22	instantiation	31, 92, 58, 60, 71, 67	⊢
	: , : , : , : , : , : , :
23	instantiation	32, 58, 54, 92, 60, 33, 71, 67, 34*	⊢
	: , : , : , : , : , :
24	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
25	instantiation	35, 77, 87	⊢
	: , :
26	instantiation	36, 65, 76, 74, 37, 38*, 39*	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
28	axiom		⊢
	proveit.logic.equality.equals_transitivity
29	instantiation	40, 41	⊢
	: , : , :
30	instantiation	42, 43, 44, 45	⊢
	: , : , : , :
31	theorem		⊢
	proveit.numbers.addition.leftward_commutation
32	theorem		⊢
	proveit.numbers.addition.association
33	instantiation	68	⊢
	: , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
35	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
36	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
37	instantiation	46, 89	⊢
	:
38	instantiation	47, 71, 51	⊢
	: , :
39	instantiation	48, 67, 49	⊢
	: , :
40	axiom		⊢
	proveit.logic.equality.substitution
41	instantiation	50, 51, 71, 52*	⊢
	: , :
42	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
43	instantiation	53, 92, 54, 55, 56, 67, 62, 71	⊢
	: , : , : , : , : , :
44	instantiation	57, 58, 59, 60, 61, 67, 62, 71	⊢
	: , : , : , :
45	instantiation	63, 71, 67, 64	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
47	theorem		⊢
	proveit.numbers.addition.commutation
48	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
49	instantiation	72	⊢
	:
50	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
51	instantiation	90, 75, 65	⊢
	: , : , :
52	instantiation	66, 67	⊢
	:
53	theorem		⊢
	proveit.numbers.addition.disassociation
54	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
55	instantiation	68	⊢
	: , :
56	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
57	theorem		⊢
	proveit.numbers.addition.elim_zero_any
58	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
60	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
61	instantiation	69	⊢
	: , : , :
62	instantiation	70, 71	⊢
	:
63	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
64	instantiation	72	⊢
	:
65	instantiation	90, 80, 73	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.negation.double_negation
67	instantiation	90, 75, 74	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
69	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
70	theorem		⊢
	proveit.numbers.negation.complex_closure
71	instantiation	90, 75, 76	⊢
	: , : , :
72	axiom		⊢
	proveit.logic.equality.equals_reflexivity
73	instantiation	90, 86, 77	⊢
	: , : , :
74	instantiation	78, 79, 89	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
76	instantiation	90, 80, 81	⊢
	: , : , :
77	instantiation	82, 83	⊢
	:
78	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
79	instantiation	84, 85	⊢
	: , :
80	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
81	instantiation	90, 86, 87	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.negation.int_closure
83	instantiation	90, 88, 89	⊢
	: , : , :
84	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
85	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
86	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
87	instantiation	90, 91, 92	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
89	assumption		⊢
90	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
91	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
92	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements