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	reference	67	⊢
2	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
3	instantiation	4, 9, 5	,  ⊢
	:
4	theorem		⊢
	proveit.numbers.exponentiation.sqrd_pos_closure
5	instantiation	6, 7	,  ⊢
	: , :
6	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
7	instantiation	8, 30, 9, 10	,  ⊢
	: , :
8	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
9	instantiation	11, 12, 13	,  ⊢
	: , :
10	instantiation	14, 15	,  ⊢
	: , :
11	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
12	instantiation	67, 55, 16	,  ⊢
	: , : , :
13	instantiation	17, 18	⊢
	:
14	theorem		⊢
	proveit.numbers.addition.subtraction.pos_difference
15	instantiation	19, 20, 21	,  ⊢
	: , : , :
16	instantiation	67, 60, 22	,  ⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.negation.real_closure
18	instantiation	23, 30, 52, 25	⊢
	: , : , :
19	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
20	instantiation	24, 30, 52, 25	⊢
	: , : , :
21	instantiation	37, 26, 27	,  ⊢
	: , : , :
22	instantiation	67, 28, 34	,  ⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
25	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
26	instantiation	29, 52, 30, 31, 32, 33*	⊢
	: , : , :
27	instantiation	44, 35, 58, 34	,  ⊢
	: , : , :
28	instantiation	53, 35, 58	⊢
	: , :
29	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
31	instantiation	67, 55, 36	⊢
	: , : , :
32	instantiation	37, 38, 39	⊢
	: , : , :
33	instantiation	40, 41, 42	⊢
	: , : , :
34	assumption		⊢
35	instantiation	57, 43, 61	⊢
	: , :
36	instantiation	67, 60, 43	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
38	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
39	instantiation	44, 61, 54, 50	⊢
	: , : , :
40	theorem		⊢
	proveit.logic.equality.sub_right_side_into
41	instantiation	45, 47	⊢
	:
42	instantiation	46, 47, 48	⊢
	: , :
43	instantiation	67, 49, 50	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
45	theorem		⊢
	proveit.numbers.addition.elim_zero_right
46	theorem		⊢
	proveit.numbers.addition.commutation
47	instantiation	67, 51, 52	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
49	instantiation	53, 61, 54	⊢
	: , :
50	assumption		⊢
51	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
52	instantiation	67, 55, 56	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
54	instantiation	57, 58, 59	⊢
	: , :
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
56	instantiation	67, 60, 61	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
58	instantiation	67, 62, 63	⊢
	: , : , :
59	instantiation	64, 65	⊢
	:
60	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
61	instantiation	67, 68, 66	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
63	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
64	theorem		⊢
	proveit.numbers.negation.int_closure
65	instantiation	67, 68, 69	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
67	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements