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*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
2	reference	29	⊢
3	instantiation	34, 35, 8	⊢
	: , :
4	instantiation	7, 35, 8, 38, 9, 10	⊢
	: , : , :
5	instantiation	61, 11, 12	⊢
	: , : , :
6	instantiation	13, 14, 15*	⊢
	: , :
7	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
8	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
9	instantiation	16, 46	⊢
	:
10	instantiation	17, 49	⊢
	:
11	instantiation	30, 18	⊢
	: , : , :
12	instantiation	19, 20	⊢
	:
13	theorem		⊢
	proveit.logic.equality.equals_reversal
14	instantiation	21, 22, 91, 67, 23, 24, 28, 32	⊢
	: , : , : , : , : , :
15	instantiation	61, 25, 26	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
17	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
18	instantiation	27, 28	⊢
	:
19	theorem		⊢
	proveit.numbers.addition.elim_zero_left
20	instantiation	89, 82, 29	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
22	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
23	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
24	instantiation	77	⊢
	: , :
25	instantiation	30, 31	⊢
	: , : , :
26	instantiation	78, 32	⊢
	:
27	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
28	instantiation	89, 82, 33	⊢
	: , : , :
29	instantiation	34, 35, 38	⊢
	: , :
30	axiom		⊢
	proveit.logic.equality.substitution
31	instantiation	36, 57, 88, 37*	⊢
	: , : , : , :
32	instantiation	89, 82, 38	⊢
	: , : , :
33	instantiation	39, 40, 83, 41	⊢
	: , :
34	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
35	instantiation	89, 85, 42	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
37	instantiation	61, 43, 44	⊢
	: , : , :
38	instantiation	89, 45, 46	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.division.div_real_closure
40	instantiation	89, 85, 47	⊢
	: , : , :
41	instantiation	65, 70	⊢
	:
42	instantiation	89, 48, 49	⊢
	: , : , :
43	instantiation	71, 91, 50, 51, 52, 53	⊢
	: , : , : , :
44	instantiation	54, 55, 56	⊢
	:
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
47	instantiation	89, 87, 57	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
49	instantiation	58, 59, 60	⊢
	: , :
50	instantiation	77	⊢
	: , :
51	instantiation	77	⊢
	: , :
52	instantiation	61, 62, 63	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
54	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
55	instantiation	89, 82, 64	⊢
	: , : , :
56	instantiation	65, 66	⊢
	:
57	instantiation	89, 90, 67	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
59	instantiation	89, 69, 68	⊢
	: , : , :
60	instantiation	89, 69, 70	⊢
	: , : , :
61	axiom		⊢
	proveit.logic.equality.equals_transitivity
62	instantiation	71, 91, 72, 73, 74, 75	⊢
	: , : , : , :
63	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
64	instantiation	89, 85, 76	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
66	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
68	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
69	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
70	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
71	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
72	instantiation	77	⊢
	: , :
73	instantiation	77	⊢
	: , :
74	instantiation	78, 80	⊢
	:
75	instantiation	79, 80	⊢
	:
76	instantiation	89, 87, 81	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
78	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
79	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
80	instantiation	89, 82, 83	⊢
	: , : , :
81	instantiation	89, 90, 84	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
83	instantiation	89, 85, 86	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
85	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
86	instantiation	89, 87, 88	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
88	instantiation	89, 90, 91	⊢
	: , : , :
89	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
90	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
91	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements