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, 37, 47, 5, 6, 7, 8, 13, 10	,  ⊢
	: , : , : , : , : , :
3	instantiation	9, 13, 10, 11	,  ⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.addition.disassociation
5	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
6	instantiation	12	⊢
	: , :
7	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
8	instantiation	14, 13	⊢
	:
9	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_21
10	instantiation	14, 15	,  ⊢
	:
11	instantiation	16	⊢
	:
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13	instantiation	45, 18, 17	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.negation.complex_closure
15	instantiation	45, 18, 19	,  ⊢
	: , : , :
16	axiom		⊢
	proveit.logic.equality.equals_reflexivity
17	instantiation	45, 21, 20	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
19	instantiation	45, 21, 22	,  ⊢
	: , : , :
20	instantiation	45, 23, 31	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
22	instantiation	45, 23, 24	,  ⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
24	instantiation	45, 25, 26	,  ⊢
	: , : , :
25	instantiation	34, 27, 28	⊢
	: , :
26	assumption		⊢
27	instantiation	38, 29, 35	⊢
	: , :
28	instantiation	43, 30	⊢
	:
29	instantiation	43, 39	⊢
	:
30	instantiation	38, 31, 35	⊢
	: , :
31	instantiation	45, 32, 33	⊢
	: , : , :
32	instantiation	34, 35, 36	⊢
	: , :
33	assumption		⊢
34	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
35	instantiation	45, 46, 37	⊢
	: , : , :
36	instantiation	38, 39, 40	⊢
	: , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
38	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
39	instantiation	45, 41, 42	⊢
	: , : , :
40	instantiation	43, 44	⊢
	:
41	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
42	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
43	theorem		⊢
	proveit.numbers.negation.int_closure
44	instantiation	45, 46, 47	⊢
	: , : , :
45	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat2