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