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	18	⊢
2	instantiation	51, 4	⊢
	: , : , :
3	instantiation	5, 69, 6, 7, 61, 8, 9, 10*	⊢
	: , : , : , : , : , :
4	instantiation	11, 64	⊢
	:
5	theorem		⊢
	proveit.numbers.multiplication.distribute_through_subtract
6	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
7	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
8	instantiation	67, 65, 12	⊢
	: , : , :
9	instantiation	13, 38, 61, 14	⊢
	: , :
10	instantiation	18, 15, 16	⊢
	: , : , :
11	axiom		⊢
	proveit.physics.quantum.QPE._delta_b_def
12	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
13	theorem		⊢
	proveit.numbers.division.div_complex_closure
14	instantiation	17, 72	⊢
	:
15	instantiation	18, 19, 20	⊢
	: , : , :
16	instantiation	21, 22, 23, 24	⊢
	: , : , : , :
17	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
18	theorem		⊢
	proveit.logic.equality.sub_right_side_into
19	instantiation	25, 37, 38, 26, 27	⊢
	: , : , : , : , :
20	instantiation	42, 28, 29	⊢
	: , : , :
21	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
22	instantiation	51, 30	⊢
	: , : , :
23	instantiation	51, 31	⊢
	: , : , :
24	instantiation	60, 38	⊢
	:
25	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
26	instantiation	67, 33, 32	⊢
	: , : , :
27	instantiation	67, 33, 34	⊢
	: , : , :
28	instantiation	51, 35	⊢
	: , : , :
29	instantiation	51, 36	⊢
	: , : , :
30	instantiation	53, 37	⊢
	:
31	instantiation	53, 38	⊢
	:
32	instantiation	67, 40, 39	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
34	instantiation	67, 40, 41	⊢
	: , : , :
35	instantiation	42, 43, 44	⊢
	: , : , :
36	instantiation	51, 45	⊢
	: , : , :
37	instantiation	67, 65, 46	⊢
	: , : , :
38	instantiation	67, 65, 47	⊢
	: , : , :
39	instantiation	67, 49, 48	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
41	instantiation	67, 49, 50	⊢
	: , : , :
42	axiom		⊢
	proveit.logic.equality.equals_transitivity
43	instantiation	51, 52	⊢
	: , : , :
44	instantiation	53, 61	⊢
	:
45	instantiation	54, 61	⊢
	:
46	instantiation	67, 56, 55	⊢
	: , : , :
47	instantiation	67, 56, 57	⊢
	: , : , :
48	instantiation	67, 58, 72	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
50	instantiation	67, 58, 59	⊢
	: , : , :
51	axiom		⊢
	proveit.logic.equality.substitution
52	instantiation	60, 61	⊢
	:
53	theorem		⊢
	proveit.numbers.division.frac_one_denom
54	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
55	instantiation	67, 63, 62	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
57	instantiation	67, 63, 64	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
59	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
60	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
61	instantiation	67, 65, 66	⊢
	: , : , :
62	instantiation	67, 68, 69	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
64	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
65	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
66	instantiation	70, 71, 72	⊢
	: , : , :
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.nat1
70	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
71	instantiation	73, 74	⊢
	: , :
72	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
73	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
74	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements