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*	⊢
	: , : , : , :
1	theorem		⊢
	proveit.core_expr_types.tuples.general_len
2	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
3	instantiation	28	⊢
	: , : , : , : , :
4	instantiation	28	⊢
	: , : , : , : , :
5	reference	21	⊢
6	instantiation	12, 10, 22	⊢
	: , : , :
7	instantiation	12, 11, 23	⊢
	: , : , :
8	instantiation	12, 13, 24	⊢
	: , : , :
9	instantiation	85, 14, 15	⊢
	: , : , :
10	instantiation	106, 17, 16	⊢
	: , : , :
11	instantiation	106, 17, 97	⊢
	: , : , :
12	theorem		⊢
	proveit.logic.equality.sub_left_side_into
13	instantiation	106, 17, 101	⊢
	: , : , :
14	instantiation	18, 19, 20, 21, 22, 23, 24	⊢
	: , : , : , :
15	instantiation	85, 25, 26	⊢
	: , : , :
16	instantiation	27, 97, 101	⊢
	: , :
17	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
18	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
19	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
20	instantiation	28	⊢
	: , : , : , : , :
21	instantiation	28	⊢
	: , : , : , : , :
22	instantiation	85, 29, 30	⊢
	: , : , :
23	instantiation	31, 75, 78, 32	⊢
	: , : , :
24	instantiation	31, 75, 82, 32	⊢
	: , : , :
25	instantiation	39, 71, 72, 33, 73, 43, 34, 78, 82	⊢
	: , : , : , : , : , :
26	instantiation	35, 36, 37, 38	⊢
	: , : , : , :
27	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
28	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
29	instantiation	39, 71, 72, 73, 43, 40, 78, 82, 41, 75	⊢
	: , : , : , : , : , :
30	instantiation	42, 72, 71, 43, 73, 78, 82, 75	⊢
	: , : , : , : , : , : , : , :
31	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
32	instantiation	44	⊢
	:
33	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
34	instantiation	45	⊢
	: , : , : , :
35	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
36	instantiation	85, 46, 47	⊢
	: , : , :
37	instantiation	70, 71, 98, 73, 48, 50, 78, 82, 49*	⊢
	: , : , : , : , : , :
38	instantiation	70, 108, 98, 71, 50, 73, 51, 82, 52*	⊢
	: , : , : , : , : , :
39	theorem		⊢
	proveit.numbers.addition.disassociation
40	instantiation	83	⊢
	: , :
41	instantiation	106, 91, 53	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general_rev
43	instantiation	83	⊢
	: , :
44	axiom		⊢
	proveit.logic.equality.equals_reflexivity
45	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
46	instantiation	55, 108, 98, 54, 78, 82	⊢
	: , : , : , : , : , : , :
47	instantiation	55, 72, 108, 56, 57, 78, 82	⊢
	: , : , : , : , : , : , :
48	instantiation	80	⊢
	: , : , :
49	instantiation	61, 58, 63*	⊢
	: , :
50	instantiation	80	⊢
	: , : , :
51	instantiation	59, 60, 78	⊢
	: , :
52	instantiation	61, 62, 63*	⊢
	: , :
53	instantiation	106, 93, 64	⊢
	: , : , :
54	instantiation	80	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.addition.leftward_commutation
56	instantiation	83	⊢
	: , :
57	instantiation	83	⊢
	: , :
58	instantiation	67, 71, 98, 108, 73, 68, 75, 78, 65*	⊢
	: , : , : , : , : , :
59	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
60	instantiation	106, 91, 66	⊢
	: , : , :
61	theorem		⊢
	proveit.logic.equality.equals_reversal
62	instantiation	67, 71, 98, 108, 73, 68, 75, 82, 69*	⊢
	: , : , : , : , : , :
63	instantiation	70, 71, 72, 108, 73, 74, 75, 76*	⊢
	: , : , : , : , : , :
64	instantiation	106, 102, 77	⊢
	: , : , :
65	instantiation	81, 78	⊢
	:
66	instantiation	106, 93, 79	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
68	instantiation	80	⊢
	: , : , :
69	instantiation	81, 82	⊢
	:
70	theorem		⊢
	proveit.numbers.addition.association
71	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
72	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
73	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
74	instantiation	83	⊢
	: , :
75	instantiation	106, 91, 84	⊢
	: , : , :
76	instantiation	85, 86, 87	⊢
	: , : , :
77	instantiation	88, 103	⊢
	:
78	instantiation	106, 91, 89	⊢
	: , : , :
79	instantiation	106, 102, 90	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
81	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
82	instantiation	106, 91, 92	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
84	instantiation	106, 93, 94	⊢
	: , : , :
85	axiom		⊢
	proveit.logic.equality.equals_transitivity
86	instantiation	95, 96	⊢
	: , : , :
87	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
88	theorem		⊢
	proveit.numbers.negation.int_closure
89	instantiation	99, 100, 97	⊢
	: , : , :
90	instantiation	106, 107, 98	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
92	instantiation	99, 100, 101	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
94	instantiation	106, 102, 103	⊢
	: , : , :
95	axiom		⊢
	proveit.logic.equality.substitution
96	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
97	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
98	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
99	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
100	instantiation	104, 105	⊢
	: , :
101	axiom		⊢
	proveit.physics.quantum.QPE._s_in_nat_pos
102	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
103	instantiation	106, 107, 108	⊢
	: , : , :
104	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
105	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
106	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
107	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
108	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements