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.multiplication.strong_bound_via_factor_bound
2	reference	84	⊢
3	reference	41	⊢
4	reference	43	⊢
5	instantiation	7, 50, 58, 8, 9, 10*, 11*	⊢
	: , : , :
6	instantiation	12, 84, 13, 14	⊢
	: , : , : , :
7	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
8	instantiation	82, 68, 15	⊢
	: , : , :
9	instantiation	16, 58, 52, 51, 17, 18	⊢
	: , : , :
10	instantiation	19, 38, 48, 20	⊢
	: , : , :
11	instantiation	21, 22, 23	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
13	instantiation	82, 73, 24	⊢
	: , : , :
14	instantiation	82, 73, 25	⊢
	: , : , :
15	instantiation	82, 75, 26	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
17	instantiation	27, 58, 51, 28, 29, 30, 31*	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
19	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
20	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
21	axiom		⊢
	proveit.logic.equality.equals_transitivity
22	instantiation	32, 33, 81, 84, 34, 35, 39, 38, 36	⊢
	: , : , : , : , : , :
23	instantiation	37, 38, 39, 40	⊢
	: , : , :
24	instantiation	82, 42, 41	⊢
	: , : , :
25	instantiation	82, 42, 43	⊢
	: , : , :
26	instantiation	82, 83, 44	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
28	instantiation	61, 62, 46	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
30	instantiation	45, 46	⊢
	:
31	instantiation	47, 48	⊢
	:
32	theorem		⊢
	proveit.numbers.addition.disassociation
33	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
34	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
35	instantiation	49	⊢
	: , :
36	instantiation	82, 73, 50	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
38	instantiation	82, 73, 51	⊢
	: , : , :
39	instantiation	82, 73, 52	⊢
	: , : , :
40	instantiation	53	⊢
	:
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
43	instantiation	54, 55	⊢
	:
44	instantiation	56, 57, 84	⊢
	: , :
45	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
46	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
47	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
48	instantiation	82, 73, 58	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
50	instantiation	82, 68, 59	⊢
	: , : , :
51	instantiation	82, 68, 60	⊢
	: , : , :
52	instantiation	61, 62, 67	⊢
	: , : , :
53	axiom		⊢
	proveit.logic.equality.equals_reflexivity
54	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
55	instantiation	63, 64, 65	⊢
	:
56	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
57	instantiation	82, 66, 67	⊢
	: , : , :
58	instantiation	82, 68, 69	⊢
	: , : , :
59	instantiation	82, 75, 70	⊢
	: , : , :
60	instantiation	82, 75, 78	⊢
	: , : , :
61	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
62	instantiation	71, 72	⊢
	: , :
63	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
64	instantiation	82, 73, 74	⊢
	: , : , :
65	assumption		⊢
66	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
67	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
68	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
69	instantiation	82, 75, 76	⊢
	: , : , :
70	instantiation	77, 78	⊢
	:
71	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
72	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
73	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
74	instantiation	79, 80	⊢
	:
75	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
76	instantiation	82, 83, 81	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.negation.int_closure
78	instantiation	82, 83, 84	⊢
	: , : , :
79	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
80	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
81	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
82	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
83	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
84	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements