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	32	⊢
2	instantiation	5, 14, 87, 80, 16, 6, 18, 17, 76	⊢
	: , : , : , : , : , :
3	instantiation	59, 7, 8	⊢
	: , : , :
4	instantiation	70, 17	⊢
	:
5	theorem		⊢
	proveit.numbers.multiplication.disassociation
6	instantiation	20	⊢
	: , :
7	instantiation	9, 14, 87, 16, 10, 18, 17, 76	⊢
	: , : , : , : , : , : , :
8	instantiation	59, 11, 12	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.multiplication.rightward_commutation
10	instantiation	20	⊢
	: , :
11	instantiation	13, 80, 87, 14, 15, 16, 17, 76, 18	⊢
	: , : , : , : , : , :
12	instantiation	67, 19	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.multiplication.association
14	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
15	instantiation	20	⊢
	: , :
16	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
17	instantiation	85, 78, 21	⊢
	: , : , :
18	instantiation	85, 78, 22	⊢
	: , : , :
19	instantiation	29, 23, 24	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
21	instantiation	25, 26, 27	⊢
	: , : , :
22	instantiation	85, 81, 28	⊢
	: , : , :
23	instantiation	29, 30, 31	⊢
	: , : , :
24	instantiation	32, 33, 34, 35	⊢
	: , : , : , :
25	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
26	instantiation	36, 37	⊢
	: , :
27	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
28	instantiation	85, 38, 39	⊢
	: , : , :
29	theorem		⊢
	proveit.logic.equality.sub_right_side_into
30	instantiation	40, 54, 41, 42	⊢
	: , : , : , : , :
31	instantiation	59, 43, 44	⊢
	: , : , :
32	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
33	instantiation	67, 45	⊢
	: , : , :
34	instantiation	67, 45	⊢
	: , : , :
35	instantiation	70, 54	⊢
	:
36	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
39	instantiation	46, 47, 48	⊢
	: , :
40	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
41	instantiation	85, 50, 49	⊢
	: , : , :
42	instantiation	85, 50, 51	⊢
	: , : , :
43	instantiation	67, 52	⊢
	: , : , :
44	instantiation	67, 53	⊢
	: , : , :
45	instantiation	69, 54	⊢
	:
46	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
47	instantiation	85, 55, 74	⊢
	: , : , :
48	instantiation	85, 55, 72	⊢
	: , : , :
49	instantiation	85, 57, 56	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
51	instantiation	85, 57, 58	⊢
	: , : , :
52	instantiation	59, 60, 61	⊢
	: , : , :
53	instantiation	67, 62	⊢
	: , : , :
54	instantiation	85, 78, 63	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
56	instantiation	85, 65, 64	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
58	instantiation	85, 65, 66	⊢
	: , : , :
59	axiom		⊢
	proveit.logic.equality.equals_transitivity
60	instantiation	67, 68	⊢
	: , : , :
61	instantiation	69, 76	⊢
	:
62	instantiation	70, 76	⊢
	:
63	instantiation	85, 81, 71	⊢
	: , : , :
64	instantiation	85, 73, 72	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
66	instantiation	85, 73, 74	⊢
	: , : , :
67	axiom		⊢
	proveit.logic.equality.substitution
68	instantiation	75, 76	⊢
	:
69	theorem		⊢
	proveit.numbers.division.frac_one_denom
70	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
71	instantiation	85, 83, 77	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
73	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
74	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
75	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
76	instantiation	85, 78, 79	⊢
	: , : , :
77	instantiation	85, 86, 80	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
79	instantiation	85, 81, 82	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
81	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
82	instantiation	85, 83, 84	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
84	instantiation	85, 86, 87	⊢
	: , : , :
85	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
86	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
87	theorem		⊢
	proveit.numbers.numerals.decimals.nat2