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	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
2	reference	24	⊢
3	instantiation	6, 50, 7	⊢
	: , :
4	instantiation	8, 17	⊢
	:
5	instantiation	9, 10, 11	⊢
	: , :
6	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
7	instantiation	12, 44	⊢
	:
8	axiom		⊢
	proveit.numbers.rounding.floor_is_an_int
9	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
10	instantiation	13, 35, 17, 14, 15*	⊢
	: , :
11	instantiation	16, 17, 50, 18	⊢
	: , :
12	theorem		⊢
	proveit.numbers.negation.int_closure
13	theorem		⊢
	proveit.numbers.rounding.floor_increasing_less_eq
14	instantiation	19, 43, 35, 27, 20, 21, 22*	⊢
	: , : , :
15	instantiation	23, 24	⊢
	:
16	theorem		⊢
	proveit.numbers.rounding.floor_of_real_below_int
17	instantiation	25, 43, 27	⊢
	: , :
18	instantiation	26, 43, 27, 36, 28, 32, 29*	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
20	instantiation	30, 35, 36, 37	⊢
	: , : , :
21	instantiation	31, 32	⊢
	: , :
22	instantiation	33, 39	⊢
	:
23	theorem		⊢
	proveit.numbers.rounding.floor_of_integer
24	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
25	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
26	theorem		⊢
	proveit.numbers.multiplication.strong_bound_via_right_factor_bound
27	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
28	instantiation	34, 35, 36, 37	⊢
	: , : , :
29	instantiation	38, 39	⊢
	:
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
31	theorem		⊢
	proveit.numbers.ordering.relax_less
32	instantiation	40, 53	⊢
	:
33	theorem		⊢
	proveit.numbers.multiplication.mult_zero_right
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
36	instantiation	51, 45, 41	⊢
	: , : , :
37	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
38	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
39	instantiation	51, 42, 43	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
41	instantiation	51, 49, 44	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
43	instantiation	51, 45, 46	⊢
	: , : , :
44	instantiation	51, 47, 48	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
46	instantiation	51, 49, 50	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
49	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
50	instantiation	51, 52, 53	⊢
	: , : , :
51	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
52	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
53	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
*equality replacement requirements