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, 9, 10, 11, 12, 13	,  ⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
2	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
3	reference	43	⊢
4	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
5	instantiation	14	⊢
	: , : , : , :
6	instantiation	15	⊢
	: , :
7	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
8	instantiation	46, 20, 16	⊢
	: , : , :
9	instantiation	46, 20, 17	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
11	instantiation	46, 20, 18	⊢
	: , : , :
12	instantiation	46, 20, 19	,  ⊢
	: , : , :
13	instantiation	46, 20, 21	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
15	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
16	instantiation	46, 26, 22	⊢
	: , : , :
17	instantiation	46, 23, 24	⊢
	: , : , :
18	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
19	instantiation	46, 26, 25	,  ⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
21	instantiation	46, 26, 27	⊢
	: , : , :
22	instantiation	46, 29, 39	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
25	instantiation	46, 29, 28	,  ⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
27	instantiation	46, 29, 36	⊢
	: , : , :
28	instantiation	46, 30, 31	,  ⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
30	instantiation	32, 33, 34	⊢
	: , :
31	assumption		⊢
32	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
33	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
34	instantiation	35, 36, 37	⊢
	: , :
35	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
36	instantiation	38, 39, 40	⊢
	: , :
37	instantiation	41, 42	⊢
	:
38	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
39	instantiation	46, 47, 43	⊢
	: , : , :
40	instantiation	46, 44, 45	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.negation.int_closure
42	instantiation	46, 47, 48	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
44	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
45	assumption		⊢
46	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
47	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat1