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	generalization	1	⊢
1	instantiation	2, 3, 4	,  ⊢
	:
2	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
3	instantiation	72, 62, 76	,  ⊢
	: , :
4	instantiation	5, 44, 12, 6, 7, 8*, 9*	,  ⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
6	instantiation	10, 48, 54	,  ⊢
	: , :
7	instantiation	11, 12, 48, 54, 13, 14	,  ⊢
	: , : , :
8	instantiation	18, 15, 16, 17	⊢
	: , : , : , :
9	instantiation	18, 19, 20, 21	,  ⊢
	: , : , : , :
10	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
11	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right
12	instantiation	79, 60, 22	⊢
	: , : , :
13	instantiation	23, 70, 71, 68	,  ⊢
	: , : , :
14	instantiation	24, 78	⊢
	:
15	instantiation	30, 37, 31, 78, 38, 25, 39, 47, 29	⊢
	: , : , : , : , : , :
16	instantiation	30, 31, 37, 25, 33, 38, 39, 47, 42, 34	⊢
	: , : , : , : , : , :
17	instantiation	26, 27, 28	⊢
	: , : , :
18	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
19	instantiation	30, 37, 31, 78, 38, 32, 35, 47, 29	,  ⊢
	: , : , : , : , : , :
20	instantiation	30, 31, 37, 32, 33, 38, 35, 47, 42, 34	,  ⊢
	: , : , : , : , : , :
21	instantiation	36, 78, 37, 38, 35, 47, 42, 40	,  ⊢
	: , : , : , : , : , : , : , :
22	instantiation	79, 66, 70	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
24	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
25	instantiation	45	⊢
	: , :
26	axiom		⊢
	proveit.logic.equality.equals_transitivity
27	instantiation	36, 78, 37, 38, 39, 47, 42, 40	⊢
	: , : , : , : , : , : , : , :
28	instantiation	41, 42, 43	⊢
	: , :
29	instantiation	79, 53, 44	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.addition.disassociation
31	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
32	instantiation	45	⊢
	: , :
33	instantiation	45	⊢
	: , :
34	instantiation	46, 47	⊢
	:
35	instantiation	79, 53, 48	,  ⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
37	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
38	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
39	instantiation	79, 53, 49	⊢
	: , : , :
40	instantiation	51	⊢
	:
41	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_reverse
42	instantiation	79, 53, 50	⊢
	: , : , :
43	instantiation	51	⊢
	:
44	instantiation	79, 60, 52	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
46	theorem		⊢
	proveit.numbers.negation.complex_closure
47	instantiation	79, 53, 54	⊢
	: , : , :
48	instantiation	79, 60, 55	,  ⊢
	: , : , :
49	instantiation	79, 60, 56	⊢
	: , : , :
50	instantiation	57, 58, 81	⊢
	: , : , :
51	axiom		⊢
	proveit.logic.equality.equals_reflexivity
52	instantiation	79, 66, 59	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
54	instantiation	79, 60, 61	⊢
	: , : , :
55	instantiation	79, 66, 62	,  ⊢
	: , : , :
56	instantiation	79, 66, 73	⊢
	: , : , :
57	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
58	instantiation	63, 64	⊢
	: , :
59	instantiation	72, 76, 65	⊢
	: , :
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
61	instantiation	79, 66, 74	⊢
	: , : , :
62	instantiation	79, 67, 68	,  ⊢
	: , : , :
63	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
65	instantiation	75, 74	⊢
	:
66	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
67	instantiation	69, 70, 71	⊢
	: , :
68	assumption		⊢
69	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
70	instantiation	72, 73, 74	⊢
	: , :
71	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
72	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
73	instantiation	75, 76	⊢
	:
74	instantiation	79, 77, 78	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.negation.int_closure
76	instantiation	79, 80, 81	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
78	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
79	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
80	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
81	assumption		⊢
*equality replacement requirements