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.weak_bound_via_left_term_bound
2	instantiation	8, 46, 68	⊢
	: , :
3	reference	60	⊢
4	reference	52	⊢
5	instantiation	9, 10	⊢
	: , :
6	instantiation	49, 11, 12	⊢
	: , : , :
7	instantiation	13, 14, 27, 15	⊢
	: , : , : , :
8	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
9	theorem		⊢
	proveit.numbers.ordering.relax_less
10	instantiation	16, 60, 61, 62	⊢
	: , : , :
11	instantiation	49, 17, 18	⊢
	: , : , :
12	instantiation	49, 19, 20	⊢
	: , : , :
13	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
14	instantiation	49, 21, 22	⊢
	: , : , :
15	instantiation	23, 32	⊢
	: , :
16	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oo_lower_bound
17	instantiation	54, 24	⊢
	: , : , :
18	instantiation	54, 28	⊢
	: , : , :
19	instantiation	33, 34, 101, 35, 36, 37, 25, 38, 41	⊢
	: , : , : , : , : , :
20	instantiation	26, 41, 38, 27	⊢
	: , : , :
21	instantiation	54, 28	⊢
	: , : , :
22	instantiation	49, 29, 30	⊢
	: , : , :
23	theorem		⊢
	proveit.logic.equality.equals_reversal
24	instantiation	54, 32	⊢
	: , : , :
25	instantiation	31, 41	⊢
	:
26	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_31
27	instantiation	48	⊢
	:
28	instantiation	54, 32	⊢
	: , : , :
29	instantiation	33, 34, 101, 35, 36, 37, 40, 38, 41	⊢
	: , : , : , : , : , :
30	instantiation	39, 40, 41, 42	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.negation.complex_closure
32	instantiation	43, 57, 72, 76, 44*	⊢
	: , :
33	theorem		⊢
	proveit.numbers.addition.disassociation
34	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
35	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
36	instantiation	45	⊢
	: , :
37	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
38	instantiation	99, 79, 46	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
40	instantiation	99, 79, 52	⊢
	: , : , :
41	instantiation	99, 79, 47	⊢
	: , : , :
42	instantiation	48	⊢
	:
43	theorem		⊢
	proveit.numbers.division.div_as_mult
44	instantiation	49, 50, 51	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
46	instantiation	67, 52	⊢
	:
47	instantiation	53, 66, 75	⊢
	: , :
48	axiom		⊢
	proveit.logic.equality.equals_reflexivity
49	axiom		⊢
	proveit.logic.equality.equals_transitivity
50	instantiation	54, 55	⊢
	: , : , :
51	instantiation	56, 57, 58	⊢
	: , :
52	instantiation	59, 60, 61, 62	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
54	axiom		⊢
	proveit.logic.equality.substitution
55	instantiation	63, 64, 96, 65*	⊢
	: , :
56	theorem		⊢
	proveit.numbers.multiplication.commutation
57	instantiation	99, 79, 75	⊢
	: , : , :
58	instantiation	99, 79, 66	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oo__is__real
60	instantiation	67, 68	⊢
	:
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
62	assumption		⊢
63	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
64	instantiation	99, 69, 70	⊢
	: , : , :
65	instantiation	71, 72	⊢
	:
66	instantiation	99, 88, 73	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.negation.real_closure
68	instantiation	74, 75, 80, 76	⊢
	: , :
69	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
70	instantiation	99, 77, 78	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
72	instantiation	99, 79, 80	⊢
	: , : , :
73	instantiation	99, 81, 82	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.division.div_real_closure
75	instantiation	99, 83, 84	⊢
	: , : , :
76	instantiation	85, 98	⊢
	:
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
78	instantiation	99, 86, 87	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
80	instantiation	99, 88, 89	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
82	instantiation	90, 91, 92	⊢
	: , :
83	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
84	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
85	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
86	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
87	instantiation	99, 93, 98	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
89	instantiation	99, 94, 95	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
91	instantiation	99, 97, 96	⊢
	: , : , :
92	instantiation	99, 97, 98	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
94	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
95	instantiation	99, 100, 101	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
97	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
98	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
99	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
100	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
101	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements