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