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	70	⊢
	: , : , :
4	instantiation	70	⊢
	: , : , :
5	instantiation	70	⊢
	: , : , :
6	instantiation	9, 100, 22	⊢
	: , : , :
7	instantiation	72, 10, 11	⊢
	: , : , :
8	instantiation	40, 12, 13	⊢
	: , : , :
9	theorem		⊢
	proveit.logic.equality.sub_left_side_into
10	instantiation	14, 15	⊢
	:
11	instantiation	48, 16, 17, 18	⊢
	: , : , : , :
12	instantiation	19, 60, 20, 21, 22, 29	⊢
	: , : , : , :
13	instantiation	40, 23, 24	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.negation.nat_closure
15	instantiation	25, 26, 27	⊢
	:
16	instantiation	53, 54, 80, 55*	⊢
	: , :
17	instantiation	52	⊢
	:
18	instantiation	28, 29	⊢
	: , :
19	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
20	instantiation	70	⊢
	: , : , :
21	instantiation	70	⊢
	: , : , :
22	instantiation	30, 80, 34	⊢
	: , : , :
23	instantiation	56, 100, 105, 31, 80, 69, 32	⊢
	: , : , : , : , : , :
24	instantiation	33, 63, 100, 65, 80, 69, 34	⊢
	: , : , : , : , : , : , : , :
25	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
26	instantiation	35, 82, 97	⊢
	: , :
27	instantiation	36, 67, 85, 76, 37, 38*, 39*	⊢
	: , : , :
28	theorem		⊢
	proveit.logic.equality.equals_reversal
29	instantiation	40, 41, 42	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
31	instantiation	71	⊢
	: , :
32	instantiation	86, 80	⊢
	:
33	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
34	instantiation	52	⊢
	:
35	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
36	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
37	instantiation	43, 96	⊢
	:
38	instantiation	79, 80, 54	⊢
	: , :
39	instantiation	44, 69, 45	⊢
	: , :
40	axiom		⊢
	proveit.logic.equality.equals_transitivity
41	instantiation	46, 47	⊢
	: , : , :
42	instantiation	48, 49, 50, 51	⊢
	: , : , : , :
43	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
44	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
45	instantiation	52	⊢
	:
46	axiom		⊢
	proveit.logic.equality.substitution
47	instantiation	53, 54, 87, 55*	⊢
	: , :
48	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
49	instantiation	56, 100, 105, 57, 58, 69, 81, 80	⊢
	: , : , : , : , : , :
50	instantiation	59, 63, 60, 65, 61, 69, 81, 80	⊢
	: , : , : , :
51	instantiation	62, 100, 105, 63, 64, 65, 69, 81, 80, 66*	⊢
	: , : , : , : , : , :
52	axiom		⊢
	proveit.logic.equality.equals_reflexivity
53	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
54	instantiation	103, 93, 67	⊢
	: , : , :
55	instantiation	68, 69	⊢
	:
56	theorem		⊢
	proveit.numbers.addition.disassociation
57	instantiation	71	⊢
	: , :
58	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
59	theorem		⊢
	proveit.numbers.addition.elim_zero_any
60	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
61	instantiation	70	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.addition.association
63	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
64	instantiation	71	⊢
	: , :
65	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
66	instantiation	72, 73, 74	⊢
	: , : , :
67	instantiation	103, 98, 75	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.negation.double_negation
69	instantiation	103, 93, 76	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
71	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
72	theorem		⊢
	proveit.logic.equality.sub_right_side_into
73	instantiation	77, 80, 87, 78	⊢
	: , : , :
74	instantiation	79, 80, 81	⊢
	: , :
75	instantiation	103, 101, 82	⊢
	: , : , :
76	instantiation	83, 84, 96	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
78	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
79	theorem		⊢
	proveit.numbers.addition.commutation
80	instantiation	103, 93, 85	⊢
	: , : , :
81	instantiation	86, 87	⊢
	:
82	instantiation	88, 89	⊢
	:
83	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
84	instantiation	90, 91	⊢
	: , :
85	instantiation	103, 98, 92	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.negation.complex_closure
87	instantiation	103, 93, 94	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.negation.int_closure
89	instantiation	103, 95, 96	⊢
	: , : , :
90	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
91	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
92	instantiation	103, 101, 97	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
94	instantiation	103, 98, 99	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
96	assumption		⊢
97	instantiation	103, 104, 100	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
99	instantiation	103, 101, 102	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
101	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
102	instantiation	103, 104, 105	⊢
	: , : , :
103	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
104	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
105	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements