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	,  ⊢
	:
1	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
2	instantiation	73, 62, 77	,  ⊢
	: , :
3	instantiation	4, 45, 11, 5, 6, 7*, 8*	,  ⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
5	instantiation	80, 65, 9	,  ⊢
	: , : , :
6	instantiation	10, 11, 49, 61, 12, 13	,  ⊢
	: , : , :
7	instantiation	17, 14, 15, 16	⊢
	: , : , : , :
8	instantiation	17, 18, 19, 20	,  ⊢
	: , : , : , :
9	instantiation	80, 69, 21	,  ⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
11	instantiation	80, 65, 22	⊢
	: , : , :
12	instantiation	23, 71, 72, 68	,  ⊢
	: , : , :
13	instantiation	24, 25	⊢
	:
14	instantiation	31, 38, 79, 37, 39, 26, 40, 48, 30	⊢
	: , : , : , : , : , :
15	instantiation	31, 79, 38, 26, 33, 39, 40, 48, 43, 34	⊢
	: , : , : , : , : , :
16	instantiation	27, 28, 29	⊢
	: , : , :
17	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
18	instantiation	31, 38, 79, 37, 39, 32, 35, 48, 30	,  ⊢
	: , : , : , : , : , :
19	instantiation	31, 79, 38, 32, 33, 39, 35, 48, 43, 34	,  ⊢
	: , : , : , : , : , :
20	instantiation	36, 37, 38, 39, 35, 48, 43, 41	,  ⊢
	: , : , : , : , : , : , : , :
21	instantiation	73, 62, 75	,  ⊢
	: , :
22	instantiation	80, 69, 71	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
24	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
25	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
26	instantiation	46	⊢
	: , :
27	axiom		⊢
	proveit.logic.equality.equals_transitivity
28	instantiation	36, 37, 38, 39, 40, 48, 43, 41	⊢
	: , : , : , : , : , : , : , :
29	instantiation	42, 43, 44	⊢
	: , :
30	instantiation	80, 55, 45	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.addition.disassociation
32	instantiation	46	⊢
	: , :
33	instantiation	46	⊢
	: , :
34	instantiation	47, 48	⊢
	:
35	instantiation	80, 55, 49	,  ⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
37	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
38	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
39	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
40	instantiation	80, 55, 50	⊢
	: , : , :
41	instantiation	51	⊢
	:
42	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_reverse
43	instantiation	80, 55, 53	⊢
	: , : , :
44	instantiation	51	⊢
	:
45	instantiation	52, 53, 54	⊢
	: , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
47	theorem		⊢
	proveit.numbers.negation.complex_closure
48	instantiation	80, 55, 61	⊢
	: , : , :
49	instantiation	80, 65, 56	,  ⊢
	: , : , :
50	instantiation	80, 65, 57	⊢
	: , : , :
51	axiom		⊢
	proveit.logic.equality.equals_reflexivity
52	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
53	instantiation	58, 59, 82	⊢
	: , : , :
54	instantiation	60, 61	⊢
	:
55	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
56	instantiation	80, 69, 62	,  ⊢
	: , : , :
57	instantiation	80, 69, 74	⊢
	: , : , :
58	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
59	instantiation	63, 64	⊢
	: , :
60	theorem		⊢
	proveit.numbers.negation.real_closure
61	instantiation	80, 65, 66	⊢
	: , : , :
62	instantiation	80, 67, 68	,  ⊢
	: , : , :
63	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
66	instantiation	80, 69, 75	⊢
	: , : , :
67	instantiation	70, 71, 72	⊢
	: , :
68	assumption		⊢
69	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
70	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
71	instantiation	73, 74, 75	⊢
	: , :
72	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
73	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
74	instantiation	76, 77	⊢
	:
75	instantiation	80, 78, 79	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.negation.int_closure
77	instantiation	80, 81, 82	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
79	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
80	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
81	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
82	assumption		⊢
*equality replacement requirements