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	21	⊢
2	instantiation	4, 85, 5, 58, 57*	⊢
	: , : , :
3	instantiation	6, 107, 7, 8, 78, 9, 10, 11*	⊢
	: , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.modular.mod_abs_scaled
5	instantiation	12, 14, 13	⊢
	: , :
6	theorem		⊢
	proveit.numbers.multiplication.distribute_through_subtract
7	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
8	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
9	instantiation	105, 84, 14	⊢
	: , : , :
10	instantiation	105, 84, 18	⊢
	: , : , :
11	instantiation	21, 15, 16	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
13	instantiation	17, 18	⊢
	:
14	instantiation	19, 59, 85, 20	⊢
	: , :
15	instantiation	21, 22, 23	⊢
	: , : , :
16	instantiation	24, 25, 26, 27	⊢
	: , : , : , :
17	theorem		⊢
	proveit.numbers.negation.real_closure
18	instantiation	28, 29, 58, 30	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.division.div_real_closure
20	instantiation	31, 32, 33	⊢
	: , :
21	theorem		⊢
	proveit.logic.equality.sub_right_side_into
22	instantiation	34, 48, 49, 35, 36	⊢
	: , : , : , : , :
23	instantiation	54, 37, 38	⊢
	: , : , :
24	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
25	instantiation	65, 39	⊢
	: , : , :
26	instantiation	65, 40	⊢
	: , : , :
27	instantiation	77, 49	⊢
	:
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
30	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
31	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
32	instantiation	105, 63, 41	⊢
	: , : , :
33	instantiation	105, 63, 42	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
35	instantiation	105, 44, 43	⊢
	: , : , :
36	instantiation	105, 44, 45	⊢
	: , : , :
37	instantiation	65, 46	⊢
	: , : , :
38	instantiation	65, 47	⊢
	: , : , :
39	instantiation	67, 48	⊢
	:
40	instantiation	67, 49	⊢
	:
41	instantiation	105, 75, 81	⊢
	: , : , :
42	instantiation	105, 75, 104	⊢
	: , : , :
43	instantiation	105, 50, 51	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
45	instantiation	105, 52, 53	⊢
	: , : , :
46	instantiation	54, 55, 56	⊢
	: , : , :
47	instantiation	65, 57	⊢
	: , : , :
48	instantiation	105, 84, 58	⊢
	: , : , :
49	instantiation	105, 84, 59	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
51	instantiation	60, 61, 62	⊢
	: , :
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
53	instantiation	105, 63, 64	⊢
	: , : , :
54	axiom		⊢
	proveit.logic.equality.equals_transitivity
55	instantiation	65, 66	⊢
	: , : , :
56	instantiation	67, 78	⊢
	:
57	instantiation	68, 78	⊢
	:
58	instantiation	105, 88, 69	⊢
	: , : , :
59	instantiation	105, 88, 70	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.exponentiation.exp_real_pos_closure
61	instantiation	105, 71, 72	⊢
	: , : , :
62	instantiation	73, 74, 104	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
64	instantiation	105, 75, 76	⊢
	: , : , :
65	axiom		⊢
	proveit.logic.equality.substitution
66	instantiation	77, 78	⊢
	:
67	theorem		⊢
	proveit.numbers.division.frac_one_denom
68	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
69	instantiation	105, 93, 101	⊢
	: , : , :
70	instantiation	105, 93, 79	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
72	instantiation	105, 80, 81	⊢
	: , : , :
73	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
74	instantiation	82, 83	⊢
	: , :
75	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
76	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
77	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
78	instantiation	105, 84, 85	⊢
	: , : , :
79	instantiation	105, 86, 87	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
81	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
82	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
83	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
84	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
85	instantiation	105, 88, 89	⊢
	: , : , :
86	instantiation	90, 91, 92	⊢
	: , :
87	assumption		⊢
88	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
89	instantiation	105, 93, 95	⊢
	: , : , :
90	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
91	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
92	instantiation	94, 95, 96	⊢
	: , :
93	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
94	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
95	instantiation	97, 98, 99	⊢
	: , :
96	instantiation	100, 101	⊢
	:
97	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
98	instantiation	105, 106, 102	⊢
	: , : , :
99	instantiation	105, 103, 104	⊢
	: , : , :
100	theorem		⊢
	proveit.numbers.negation.int_closure
101	instantiation	105, 106, 107	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
103	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
104	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
105	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
106	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
107	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements