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	⊢
	: , : , : , :
1	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
2	instantiation	41, 5, 6	⊢
	: , : , :
3	instantiation	27, 28, 53, 30, 7, 9, 34, 38, 8*	⊢
	: , : , : , : , : , :
4	instantiation	27, 63, 53, 28, 9, 30, 10, 38, 11*	⊢
	: , : , : , : , : , :
5	instantiation	13, 63, 53, 12, 34, 38	⊢
	: , : , : , : , : , : , :
6	instantiation	13, 29, 63, 14, 15, 34, 38	⊢
	: , : , : , : , : , : , :
7	instantiation	36	⊢
	: , : , :
8	instantiation	19, 16, 21*	⊢
	: , :
9	instantiation	36	⊢
	: , : , :
10	instantiation	17, 18, 34	⊢
	: , :
11	instantiation	19, 20, 21*	⊢
	: , :
12	instantiation	36	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.addition.leftward_commutation
14	instantiation	39	⊢
	: , :
15	instantiation	39	⊢
	: , :
16	instantiation	24, 28, 53, 63, 30, 25, 32, 34, 22*	⊢
	: , : , : , : , : , :
17	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
18	instantiation	61, 46, 23	⊢
	: , : , :
19	theorem		⊢
	proveit.logic.equality.equals_reversal
20	instantiation	24, 28, 53, 63, 30, 25, 32, 38, 26*	⊢
	: , : , : , : , : , :
21	instantiation	27, 28, 29, 63, 30, 31, 32, 33*	⊢
	: , : , : , : , : , :
22	instantiation	37, 34	⊢
	:
23	instantiation	61, 48, 35	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
25	instantiation	36	⊢
	: , : , :
26	instantiation	37, 38	⊢
	:
27	theorem		⊢
	proveit.numbers.addition.association
28	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
29	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
30	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
31	instantiation	39	⊢
	: , :
32	instantiation	61, 46, 40	⊢
	: , : , :
33	instantiation	41, 42, 43	⊢
	: , : , :
34	instantiation	61, 46, 44	⊢
	: , : , :
35	instantiation	61, 57, 45	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
37	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
38	instantiation	61, 46, 47	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
40	instantiation	61, 48, 49	⊢
	: , : , :
41	axiom		⊢
	proveit.logic.equality.equals_transitivity
42	instantiation	50, 51	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
44	instantiation	54, 55, 52	⊢
	: , : , :
45	instantiation	61, 62, 53	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
47	instantiation	54, 55, 56	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
49	instantiation	61, 57, 58	⊢
	: , : , :
50	axiom		⊢
	proveit.logic.equality.substitution
51	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
52	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
54	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
55	instantiation	59, 60	⊢
	: , :
56	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
57	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
58	instantiation	61, 62, 63	⊢
	: , : , :
59	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
61	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
62	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements