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	⊢
	: , : , : , :
1	theorem		⊢
	proveit.core_expr_types.tuples.partition
2	instantiation	5, 6, 7	⊢
	:
3	instantiation	8, 9, 10	⊢
	: , :
4	reference	45	⊢
5	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
6	instantiation	17, 11, 12	⊢
	: , :
7	instantiation	13, 14	⊢
	: , :
8	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
9	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
10	instantiation	83, 15, 16	⊢
	: , : , :
11	instantiation	17, 18, 77	⊢
	: , :
12	instantiation	83, 19, 20	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
14	instantiation	21, 46, 22, 47, 23, 24*, 25*	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
16	instantiation	28, 27	⊢
	:
17	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
18	instantiation	83, 26, 27	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
20	instantiation	28, 69	⊢
	:
21	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
23	instantiation	29, 70	⊢
	:
24	instantiation	49, 30, 31	⊢
	: , : , :
25	instantiation	32, 33, 34, 35	⊢
	: , : , : , :
26	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
27	instantiation	75, 36	⊢
	:
28	theorem		⊢
	proveit.numbers.negation.nat_pos_closure
29	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
30	instantiation	37, 38	⊢
	:
31	instantiation	58, 38, 39	⊢
	: , :
32	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
33	instantiation	56, 59, 40, 41, 42	⊢
	: , : , :
34	instantiation	43	⊢
	:
35	instantiation	44, 45	⊢
	: , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
37	theorem		⊢
	proveit.numbers.addition.elim_zero_right
38	instantiation	83, 73, 46	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
40	instantiation	83, 73, 47	⊢
	: , : , :
41	instantiation	83, 73, 48	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_3
43	axiom		⊢
	proveit.logic.equality.equals_reflexivity
44	theorem		⊢
	proveit.logic.equality.equals_reversal
45	instantiation	49, 50, 51	⊢
	: , : , :
46	instantiation	83, 52, 53	⊢
	: , : , :
47	instantiation	83, 78, 54	⊢
	: , : , :
48	instantiation	83, 78, 55	⊢
	: , : , :
49	theorem		⊢
	proveit.logic.equality.sub_right_side_into
50	instantiation	56, 59, 67, 57	⊢
	: , : , :
51	instantiation	58, 59, 60	⊢
	: , :
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
53	instantiation	83, 61, 62	⊢
	: , : , :
54	instantiation	83, 81, 63	⊢
	: , : , :
55	instantiation	83, 81, 64	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
57	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
58	theorem		⊢
	proveit.numbers.addition.commutation
59	instantiation	83, 73, 65	⊢
	: , : , :
60	instantiation	66, 67	⊢
	:
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
62	instantiation	83, 68, 69	⊢
	: , : , :
63	instantiation	83, 84, 70	⊢
	: , : , :
64	instantiation	83, 84, 71	⊢
	: , : , :
65	instantiation	83, 78, 72	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.negation.complex_closure
67	instantiation	83, 73, 74	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
69	instantiation	75, 76	⊢
	:
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
72	instantiation	83, 81, 77	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
74	instantiation	83, 78, 79	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.negation.int_neg_closure
76	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
77	instantiation	83, 84, 80	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
79	instantiation	83, 81, 82	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
81	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
82	instantiation	83, 84, 85	⊢
	: , : , :
83	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
84	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
85	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements