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	generalization	1	⊢
1	instantiation	2, 3, 4, 5, 6	,  ⊢
	: , : , :
2	theorem		⊢
	proveit.numbers.division.strong_div_from_denom_bound__all_pos
3	instantiation	135, 8, 7	⊢
	: , : , :
4	instantiation	135, 8, 9	,  ⊢
	: , : , :
5	instantiation	10, 27, 11	,  ⊢
	:
6	instantiation	12, 101, 13, 27, 14, 15	,  ⊢
	: , : , :
7	instantiation	135, 16, 71	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
9	instantiation	135, 16, 17	,  ⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.exponentiation.sqrd_pos_closure
11	instantiation	18, 19	,  ⊢
	: , :
12	theorem		⊢
	proveit.numbers.exponentiation.exp_pos_less
13	instantiation	34, 35, 39	,  ⊢
	: , :
14	instantiation	20, 33, 21	,  ⊢
	: , :
15	instantiation	22, 23	⊢
	:
16	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
17	instantiation	24, 25, 137	,  ⊢
	: , :
18	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
19	instantiation	26, 83, 27, 28	,  ⊢
	: , :
20	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
21	instantiation	29, 35, 39, 36, 30	,  ⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
23	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
24	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
25	instantiation	31, 32, 33	,  ⊢
	:
26	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
27	instantiation	34, 35, 36	,  ⊢
	: , :
28	instantiation	59, 37	,  ⊢
	: , :
29	theorem		⊢
	proveit.numbers.addition.strong_bound_via_right_term_bound
30	instantiation	38, 39, 47, 118, 49, 40, 41*, 42*	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
32	instantiation	125, 61, 43	,  ⊢
	: , :
33	instantiation	44, 45	,  ⊢
	: , :
34	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
35	instantiation	135, 123, 46	,  ⊢
	: , : , :
36	instantiation	50, 47	⊢
	:
37	instantiation	48, 49, 60	,  ⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.multiplication.reversed_strong_bound_via_right_factor_bound
39	instantiation	50, 118	⊢
	:
40	instantiation	51, 58	⊢
	:
41	instantiation	52, 109, 53*	⊢
	: , :
42	instantiation	54, 55, 56	⊢
	: , : , :
43	instantiation	135, 57, 58	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.ordering.relax_less
45	instantiation	59, 60	,  ⊢
	: , :
46	instantiation	135, 128, 61	,  ⊢
	: , : , :
47	instantiation	62, 83, 118, 64	⊢
	: , : , :
48	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
49	instantiation	63, 83, 118, 64	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.negation.real_closure
51	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
52	theorem		⊢
	proveit.numbers.multiplication.mult_neg_left
53	instantiation	65, 109	⊢
	:
54	axiom		⊢
	proveit.logic.equality.equals_transitivity
55	instantiation	66, 134, 137, 77, 79, 78, 67, 80, 81	⊢
	: , : , : , : , : , :
56	instantiation	68, 77, 137, 78, 79, 109, 80, 81, 69*	⊢
	: , : , : , : , :
57	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
58	instantiation	70, 71	⊢
	:
59	theorem		⊢
	proveit.numbers.addition.subtraction.pos_difference
60	instantiation	95, 72, 73	,  ⊢
	: , : , :
61	instantiation	135, 74, 87	,  ⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
63	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_co_upper_bound
64	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
65	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
66	theorem		⊢
	proveit.numbers.multiplication.disassociation
67	instantiation	75, 109	⊢
	:
68	theorem		⊢
	proveit.numbers.multiplication.mult_neg_any
69	instantiation	76, 77, 137, 78, 79, 80, 81	⊢
	: , : , : , :
70	theorem		⊢
	proveit.numbers.negation.int_neg_closure
71	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
72	instantiation	82, 118, 83, 84, 85, 86*	⊢
	: , : , :
73	instantiation	106, 88, 126, 87	,  ⊢
	: , : , :
74	instantiation	121, 88, 126	⊢
	: , :
75	theorem		⊢
	proveit.numbers.negation.complex_closure
76	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
77	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
78	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
79	instantiation	89	⊢
	: , :
80	instantiation	90, 91, 92	⊢
	: , :
81	instantiation	135, 117, 93	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
83	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
84	instantiation	135, 123, 94	⊢
	: , : , :
85	instantiation	95, 96, 97	⊢
	: , : , :
86	instantiation	98, 99, 100	⊢
	: , : , :
87	assumption		⊢
88	instantiation	125, 105, 129	⊢
	: , :
89	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
90	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
91	instantiation	135, 117, 101	⊢
	: , : , :
92	instantiation	135, 117, 102	⊢
	: , : , :
93	instantiation	103, 104	⊢
	:
94	instantiation	135, 128, 105	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
96	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
97	instantiation	106, 129, 122, 116	⊢
	: , : , :
98	theorem		⊢
	proveit.logic.equality.sub_right_side_into
99	instantiation	107, 109	⊢
	:
100	instantiation	108, 109, 110	⊢
	: , :
101	instantiation	135, 123, 111	⊢
	: , : , :
102	instantiation	112, 113, 114	⊢
	: , : , :
103	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
104	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
105	instantiation	135, 115, 116	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
107	theorem		⊢
	proveit.numbers.addition.elim_zero_right
108	theorem		⊢
	proveit.numbers.addition.commutation
109	instantiation	135, 117, 118	⊢
	: , : , :
110	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
111	instantiation	135, 128, 133	⊢
	: , : , :
112	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
113	instantiation	119, 120	⊢
	: , :
114	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
115	instantiation	121, 129, 122	⊢
	: , :
116	assumption		⊢
117	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
118	instantiation	135, 123, 124	⊢
	: , : , :
119	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
120	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
121	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
122	instantiation	125, 126, 127	⊢
	: , :
123	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
124	instantiation	135, 128, 129	⊢
	: , : , :
125	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
126	instantiation	135, 130, 131	⊢
	: , : , :
127	instantiation	132, 133	⊢
	:
128	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
129	instantiation	135, 136, 134	⊢
	: , : , :
130	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
131	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
132	theorem		⊢
	proveit.numbers.negation.int_closure
133	instantiation	135, 136, 137	⊢
	: , : , :
134	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
135	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
136	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
137	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements