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	reference	5	⊢
2	instantiation	5, 6, 7, 8	⊢
	: , : , : , :
3	instantiation	49, 50, 57, 51, 9, 11, 38, 42, 10*	⊢
	: , : , : , : , : , :
4	instantiation	49, 81, 57, 50, 11, 51, 12, 42, 13*	⊢
	: , : , : , : , : , :
5	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
6	instantiation	19, 81, 14, 15, 38, 42	⊢
	: , : , : , : , : , : , :
7	instantiation	19, 78, 20, 16, 17, 18, 38, 42	⊢
	: , : , : , : , : , : , :
8	instantiation	19, 20, 81, 21, 22, 38, 42	⊢
	: , : , : , : , : , : , :
9	instantiation	40	⊢
	: , : , : , :
10	instantiation	26, 23, 28*	⊢
	: , :
11	instantiation	40	⊢
	: , : , : , :
12	instantiation	24, 25, 38	⊢
	: , :
13	instantiation	26, 27, 28*	⊢
	: , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
15	instantiation	29	⊢
	: , : , : , : , :
16	instantiation	61	⊢
	: , :
17	instantiation	61	⊢
	: , :
18	instantiation	30	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.addition.leftward_commutation
20	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
21	instantiation	30	⊢
	: , : , :
22	instantiation	30	⊢
	: , : , :
23	instantiation	33, 50, 57, 81, 51, 34, 54, 38, 31*	⊢
	: , : , : , : , : , :
24	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
25	instantiation	79, 63, 32	⊢
	: , : , :
26	theorem		⊢
	proveit.logic.equality.equals_reversal
27	instantiation	33, 50, 57, 81, 51, 34, 54, 42, 35*	⊢
	: , : , : , : , : , :
28	instantiation	49, 50, 78, 51, 36, 54, 37*	⊢
	: , : , : , : , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
30	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
31	instantiation	41, 38	⊢
	:
32	instantiation	79, 71, 39	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
34	instantiation	40	⊢
	: , : , : , :
35	instantiation	41, 42	⊢
	:
36	instantiation	61	⊢
	: , :
37	instantiation	65, 43, 44	⊢
	: , : , :
38	instantiation	79, 63, 45	⊢
	: , : , :
39	instantiation	79, 76, 46	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
41	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
42	instantiation	79, 63, 47	⊢
	: , : , :
43	instantiation	73, 48	⊢
	: , : , :
44	instantiation	49, 50, 78, 81, 51, 52, 53, 54, 55*	⊢
	: , : , : , : , : , :
45	instantiation	58, 59, 56	⊢
	: , : , :
46	instantiation	79, 80, 57	⊢
	: , : , :
47	instantiation	58, 59, 60	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
49	theorem		⊢
	proveit.numbers.addition.association
50	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
51	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
52	instantiation	61	⊢
	: , :
53	instantiation	79, 63, 62	⊢
	: , : , :
54	instantiation	79, 63, 64	⊢
	: , : , :
55	instantiation	65, 66, 67	⊢
	: , : , :
56	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
58	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
59	instantiation	68, 69	⊢
	: , :
60	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
61	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
62	instantiation	79, 71, 70	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
64	instantiation	79, 71, 72	⊢
	: , : , :
65	axiom		⊢
	proveit.logic.equality.equals_transitivity
66	instantiation	73, 74	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
68	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
69	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
70	instantiation	79, 76, 75	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
72	instantiation	79, 76, 77	⊢
	: , : , :
73	axiom		⊢
	proveit.logic.equality.substitution
74	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
75	instantiation	79, 80, 78	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
77	instantiation	79, 80, 81	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
79	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
80	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
81	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements