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*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
2	instantiation	8, 41	⊢
	:
3	reference	43	⊢
4	instantiation	9, 37, 41	⊢
	: , :
5	instantiation	10, 43, 37, 41, 11, 12	⊢
	: , : , :
6	instantiation	13, 33, 36, 14, 15	⊢
	: , : , :
7	instantiation	16, 17, 18	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.negation.real_closure
9	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
10	theorem		⊢
	proveit.numbers.ordering.less_add_right
11	instantiation	19, 43, 44, 45	⊢
	: , : , :
12	instantiation	20, 57	⊢
	:
13	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
14	instantiation	59, 40, 43	⊢
	: , : , :
15	instantiation	21, 22, 23	⊢
	: , : , :
16	axiom		⊢
	proveit.logic.equality.equals_transitivity
17	instantiation	24, 25, 56, 57, 26, 27, 30, 36, 28	⊢
	: , : , : , : , : , :
18	instantiation	29, 36, 30, 31	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oo_lower_bound
20	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
21	theorem		⊢
	proveit.logic.equality.sub_right_side_into
22	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_2
23	instantiation	32, 36, 33	⊢
	: , :
24	theorem		⊢
	proveit.numbers.addition.disassociation
25	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
26	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
27	instantiation	34	⊢
	: , :
28	instantiation	35, 36	⊢
	:
29	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
30	instantiation	59, 40, 37	⊢
	: , : , :
31	instantiation	38	⊢
	:
32	theorem		⊢
	proveit.numbers.addition.commutation
33	instantiation	59, 40, 39	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
35	theorem		⊢
	proveit.numbers.negation.complex_closure
36	instantiation	59, 40, 41	⊢
	: , : , :
37	instantiation	42, 43, 44, 45	⊢
	: , : , :
38	axiom		⊢
	proveit.logic.equality.equals_reflexivity
39	instantiation	59, 49, 46	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
41	instantiation	59, 49, 47	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oo__is__real
43	instantiation	59, 49, 48	⊢
	: , : , :
44	instantiation	59, 49, 50	⊢
	: , : , :
45	assumption		⊢
46	instantiation	59, 54, 51	⊢
	: , : , :
47	instantiation	59, 54, 52	⊢
	: , : , :
48	instantiation	59, 54, 53	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
50	instantiation	59, 54, 55	⊢
	: , : , :
51	instantiation	59, 60, 56	⊢
	: , : , :
52	instantiation	59, 60, 57	⊢
	: , : , :
53	instantiation	59, 60, 58	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
55	instantiation	59, 60, 61	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
58	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
59	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
60	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
*equality replacement requirements