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	,  ⊢
	: , : , :
1	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
2	instantiation	4, 9, 31, 5	⊢
	: , : , :
3	instantiation	16, 6, 7	,  ⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
5	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
6	instantiation	8, 31, 9, 10, 11, 12*	⊢
	: , : , :
7	instantiation	23, 13, 37, 14	,  ⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
9	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
10	instantiation	46, 34, 15	⊢
	: , : , :
11	instantiation	16, 17, 18	⊢
	: , : , :
12	instantiation	19, 20, 21	⊢
	: , : , :
13	instantiation	36, 22, 40	⊢
	: , :
14	assumption		⊢
15	instantiation	46, 39, 22	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
17	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
18	instantiation	23, 40, 33, 29	⊢
	: , : , :
19	theorem		⊢
	proveit.logic.equality.sub_right_side_into
20	instantiation	24, 26	⊢
	:
21	instantiation	25, 26, 27	⊢
	: , :
22	instantiation	46, 28, 29	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
24	theorem		⊢
	proveit.numbers.addition.elim_zero_right
25	theorem		⊢
	proveit.numbers.addition.commutation
26	instantiation	46, 30, 31	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
28	instantiation	32, 40, 33	⊢
	: , :
29	assumption		⊢
30	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
31	instantiation	46, 34, 35	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
33	instantiation	36, 37, 38	⊢
	: , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
35	instantiation	46, 39, 40	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
37	instantiation	46, 41, 42	⊢
	: , : , :
38	instantiation	43, 44	⊢
	:
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
40	instantiation	46, 47, 45	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
42	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
43	theorem		⊢
	proveit.numbers.negation.int_closure
44	instantiation	46, 47, 48	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
46	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
47	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements