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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	4, 72, 67, 5, 6, 7, 10, 11, 8	⊢
	: , : , : , : , : , :
3	instantiation	9, 10, 11, 12	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.addition.disassociation
5	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
6	instantiation	13	⊢
	: , :
7	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
8	instantiation	70, 15, 14	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
10	instantiation	70, 15, 18	⊢
	: , : , :
11	instantiation	70, 15, 16	⊢
	: , : , :
12	instantiation	17	⊢
	:
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
14	instantiation	31, 18	⊢
	:
15	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
16	instantiation	20, 19, 51, 22	⊢
	: , :
17	axiom		⊢
	proveit.logic.equality.equals_reflexivity
18	instantiation	20, 21, 51, 22	⊢
	: , :
19	instantiation	24, 25, 23	⊢
	: , :
20	theorem		⊢
	proveit.numbers.modular.mod_abs_real_closure
21	instantiation	24, 25, 26	⊢
	: , :
22	instantiation	27, 28, 29	⊢
	: , :
23	instantiation	31, 47	⊢
	:
24	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
25	instantiation	70, 60, 30	⊢
	: , : , :
26	instantiation	31, 32	⊢
	:
27	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
28	instantiation	70, 34, 33	⊢
	: , : , :
29	instantiation	70, 34, 35	⊢
	: , : , :
30	instantiation	70, 65, 36	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.negation.real_closure
32	instantiation	70, 60, 37	⊢
	: , : , :
33	instantiation	70, 39, 38	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
35	instantiation	70, 39, 69	⊢
	: , : , :
36	instantiation	70, 40, 41	⊢
	: , : , :
37	instantiation	70, 65, 42	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
39	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
40	instantiation	43, 44, 45	⊢
	: , :
41	assumption		⊢
42	instantiation	46, 47	⊢
	:
43	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
44	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
45	instantiation	48, 59, 49	⊢
	: , :
46	axiom		⊢
	proveit.numbers.rounding.floor_is_an_int
47	instantiation	50, 51, 52	⊢
	: , :
48	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
49	instantiation	53, 66	⊢
	:
50	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
51	instantiation	70, 60, 54	⊢
	: , : , :
52	instantiation	55, 56, 57, 58	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.negation.int_closure
54	instantiation	70, 65, 59	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
57	instantiation	70, 60, 61	⊢
	: , : , :
58	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
59	instantiation	62, 63, 64	⊢
	: , :
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
61	instantiation	70, 65, 66	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
63	instantiation	70, 71, 67	⊢
	: , : , :
64	instantiation	70, 68, 69	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
66	instantiation	70, 71, 72	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
68	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
69	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
70	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
71	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
72	theorem		⊢
	proveit.numbers.numerals.decimals.nat1