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	39	⊢
2	modus ponens	4, 5	⊢
3	modus ponens	6, 7	⊢
4	instantiation	9	⊢
	: , : , :
5	generalization	8	⊢
6	instantiation	9	⊢
	: , : , :
7	generalization	10	⊢
8	instantiation	13, 97, 11, 12	,  ⊢
	: , :
9	theorem		⊢
	proveit.numbers.summation.summation_real_closure
10	instantiation	13, 97, 14, 15	,  ⊢
	: , :
11	instantiation	17, 26, 116	,  ⊢
	: , :
12	instantiation	18, 16	,  ⊢
	:
13	theorem		⊢
	proveit.numbers.division.div_real_closure
14	instantiation	17, 34, 116	,  ⊢
	: , :
15	instantiation	18, 19	,  ⊢
	:
16	instantiation	114, 21, 20	,  ⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
19	instantiation	114, 21, 22	,  ⊢
	: , : , :
20	instantiation	24, 26, 23	,  ⊢
	:
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
22	instantiation	24, 34, 25	,  ⊢
	:
23	instantiation	33, 26, 72, 27	,  ⊢
	: , :
24	theorem		⊢
	proveit.numbers.exponentiation.sqrd_pos_closure
25	instantiation	28, 29	,  ⊢
	: , :
26	instantiation	39, 30, 41	,  ⊢
	: , :
27	instantiation	31, 32	,  ⊢
	: , :
28	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
29	instantiation	33, 72, 34, 35	,  ⊢
	: , :
30	instantiation	114, 102, 36	,  ⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.addition.subtraction.neg_difference
32	instantiation	92, 37, 38	,  ⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
34	instantiation	39, 40, 41	,  ⊢
	: , :
35	instantiation	42, 43	,  ⊢
	: , :
36	instantiation	114, 107, 44	,  ⊢
	: , : , :
37	instantiation	45, 46, 47	,  ⊢
	: , : , :
38	instantiation	48, 72, 97, 63	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
40	instantiation	114, 102, 49	,  ⊢
	: , : , :
41	instantiation	50, 51	⊢
	:
42	theorem		⊢
	proveit.numbers.addition.subtraction.pos_difference
43	instantiation	52, 53, 54	,  ⊢
	: , : , :
44	instantiation	114, 55, 57	,  ⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
46	instantiation	56, 66, 67, 57	,  ⊢
	: , : , :
47	instantiation	58, 59	⊢
	:
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_lower_bound
49	instantiation	114, 107, 60	,  ⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.negation.real_closure
51	instantiation	61, 72, 97, 63	⊢
	: , : , :
52	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
53	instantiation	62, 72, 97, 63	⊢
	: , : , :
54	instantiation	92, 64, 65	,  ⊢
	: , : , :
55	instantiation	100, 66, 67	⊢
	: , :
56	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
57	assumption		⊢
58	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
59	instantiation	68, 69	⊢
	:
60	instantiation	114, 70, 75	,  ⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
63	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
64	instantiation	71, 97, 72, 73, 86, 74*	⊢
	: , : , :
65	instantiation	98, 80, 105, 75	,  ⊢
	: , : , :
66	instantiation	104, 76, 108	⊢
	: , :
67	instantiation	111, 80	⊢
	:
68	theorem		⊢
	proveit.numbers.negation.int_neg_closure
69	instantiation	77, 78, 79	⊢
	: , :
70	instantiation	100, 80, 105	⊢
	: , :
71	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
72	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
73	instantiation	114, 102, 81	⊢
	: , : , :
74	instantiation	82, 83, 84	⊢
	: , : , :
75	assumption		⊢
76	instantiation	111, 105	⊢
	:
77	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
78	instantiation	85, 87, 86	⊢
	:
79	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
80	instantiation	104, 87, 108	⊢
	: , :
81	instantiation	114, 107, 87	⊢
	: , : , :
82	theorem		⊢
	proveit.logic.equality.sub_right_side_into
83	instantiation	88, 90	⊢
	:
84	instantiation	89, 90, 91	⊢
	: , :
85	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
86	instantiation	92, 93, 94	⊢
	: , : , :
87	instantiation	114, 95, 99	⊢
	: , : , :
88	theorem		⊢
	proveit.numbers.addition.elim_zero_right
89	theorem		⊢
	proveit.numbers.addition.commutation
90	instantiation	114, 96, 97	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
92	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
93	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
94	instantiation	98, 108, 101, 99	⊢
	: , : , :
95	instantiation	100, 108, 101	⊢
	: , :
96	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
97	instantiation	114, 102, 103	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
99	assumption		⊢
100	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
101	instantiation	104, 105, 106	⊢
	: , :
102	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
103	instantiation	114, 107, 108	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
105	instantiation	114, 109, 110	⊢
	: , : , :
106	instantiation	111, 112	⊢
	:
107	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
108	instantiation	114, 115, 113	⊢
	: , : , :
109	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
110	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
111	theorem		⊢
	proveit.numbers.negation.int_closure
112	instantiation	114, 115, 116	⊢
	: , : , :
113	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
114	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
115	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
116	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements