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	84, 69, 108, 86	⊢
	: , :
3	instantiation	43, 44, 9	⊢
	: , :
4	reference	38	⊢
5	instantiation	8, 44, 9, 69, 10, 11	⊢
	: , : , :
6	instantiation	12, 13, 14, 15	⊢
	: , : , : , :
7	instantiation	74, 16, 17	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
9	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
10	instantiation	18, 83	⊢
	:
11	instantiation	19, 58	⊢
	:
12	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
13	instantiation	74, 20, 21	⊢
	: , : , :
14	instantiation	22	⊢
	:
15	instantiation	23, 37	⊢
	: , :
16	instantiation	52, 37	⊢
	: , : , :
17	instantiation	23, 24, 25*	⊢
	: , :
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.positive_if_in_real_pos
19	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
20	instantiation	74, 26, 27	⊢
	: , : , :
21	instantiation	28, 29	⊢
	:
22	axiom		⊢
	proveit.logic.equality.equals_reflexivity
23	theorem		⊢
	proveit.logic.equality.equals_reversal
24	instantiation	30, 31, 119, 112, 32, 33, 56, 55	⊢
	: , : , : , : , : , :
25	instantiation	74, 34, 35	⊢
	: , : , :
26	instantiation	52, 36	⊢
	: , : , :
27	instantiation	52, 37	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.addition.elim_zero_left
29	instantiation	117, 107, 38	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
31	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
32	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
33	instantiation	99	⊢
	: , :
34	instantiation	52, 39	⊢
	: , : , :
35	instantiation	100, 55	⊢
	:
36	instantiation	40, 56	⊢
	:
37	instantiation	41, 55, 102, 86, 42*	⊢
	: , :
38	instantiation	43, 44, 69	⊢
	: , :
39	instantiation	45, 106, 116, 46*	⊢
	: , : , : , :
40	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
41	theorem		⊢
	proveit.numbers.division.div_as_mult
42	instantiation	74, 47, 48	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
44	instantiation	117, 113, 49	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
46	instantiation	74, 50, 51	⊢
	: , : , :
47	instantiation	52, 53	⊢
	: , : , :
48	instantiation	54, 55, 56	⊢
	: , :
49	instantiation	117, 57, 58	⊢
	: , : , :
50	instantiation	89, 119, 59, 60, 61, 62	⊢
	: , : , : , :
51	instantiation	63, 64, 65	⊢
	:
52	axiom		⊢
	proveit.logic.equality.substitution
53	instantiation	66, 67, 87, 68*	⊢
	: , :
54	theorem		⊢
	proveit.numbers.multiplication.commutation
55	instantiation	117, 107, 69	⊢
	: , : , :
56	instantiation	117, 107, 70	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
58	instantiation	71, 72, 73	⊢
	: , :
59	instantiation	99	⊢
	: , :
60	instantiation	99	⊢
	: , :
61	instantiation	74, 75, 76	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
63	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
64	instantiation	117, 107, 77	⊢
	: , : , :
65	instantiation	98, 78	⊢
	:
66	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
67	instantiation	117, 79, 80	⊢
	: , : , :
68	instantiation	81, 102	⊢
	:
69	instantiation	117, 82, 83	⊢
	: , : , :
70	instantiation	84, 85, 108, 86	⊢
	: , :
71	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
72	instantiation	117, 88, 87	⊢
	: , : , :
73	instantiation	117, 88, 111	⊢
	: , : , :
74	axiom		⊢
	proveit.logic.equality.equals_transitivity
75	instantiation	89, 119, 90, 91, 92, 93	⊢
	: , : , : , :
76	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
77	instantiation	117, 113, 94	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
79	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
80	instantiation	117, 95, 96	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
82	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
83	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
84	theorem		⊢
	proveit.numbers.division.div_real_closure
85	instantiation	117, 113, 97	⊢
	: , : , :
86	instantiation	98, 111	⊢
	:
87	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
88	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
89	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
90	instantiation	99	⊢
	: , :
91	instantiation	99	⊢
	: , :
92	instantiation	100, 102	⊢
	:
93	instantiation	101, 102	⊢
	:
94	instantiation	117, 115, 103	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
96	instantiation	117, 104, 105	⊢
	: , : , :
97	instantiation	117, 115, 106	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
99	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
100	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
101	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
102	instantiation	117, 107, 108	⊢
	: , : , :
103	instantiation	117, 118, 109	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
105	instantiation	117, 110, 111	⊢
	: , : , :
106	instantiation	117, 118, 112	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
108	instantiation	117, 113, 114	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
110	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
111	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
112	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
113	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
114	instantiation	117, 115, 116	⊢
	: , : , :
115	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
116	instantiation	117, 118, 119	⊢
	: , : , :
117	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
118	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
119	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements