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, 10*, 11*	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
2	reference	79	⊢
3	reference	45	⊢
4	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
5	instantiation	12	⊢
	: , :
6	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7	reference	66	⊢
8	reference	15	⊢
9	instantiation	77, 67, 13	⊢
	: , : , :
10	instantiation	14, 66, 15	⊢
	: , :
11	instantiation	21, 16, 17	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13	instantiation	18, 71, 68, 19	⊢
	: , :
14	theorem		⊢
	proveit.numbers.multiplication.commutation
15	instantiation	77, 67, 20	⊢
	: , : , :
16	instantiation	21, 22, 23	⊢
	: , : , :
17	instantiation	24, 25, 26, 27	⊢
	: , : , : , :
18	theorem		⊢
	proveit.numbers.division.div_real_closure
19	instantiation	28, 29	⊢
	: , :
20	instantiation	77, 73, 30	⊢
	: , : , :
21	theorem		⊢
	proveit.logic.equality.sub_right_side_into
22	instantiation	31, 44, 32, 33	⊢
	: , : , : , : , :
23	instantiation	50, 34, 35	⊢
	: , : , :
24	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
25	instantiation	58, 36	⊢
	: , : , :
26	instantiation	58, 36	⊢
	: , : , :
27	instantiation	61, 44	⊢
	:
28	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
29	instantiation	37, 70, 68, 55	⊢
	: , :
30	instantiation	77, 75, 38	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
32	instantiation	77, 40, 39	⊢
	: , : , :
33	instantiation	77, 40, 41	⊢
	: , : , :
34	instantiation	58, 42	⊢
	: , : , :
35	instantiation	58, 43	⊢
	: , : , :
36	instantiation	60, 44	⊢
	:
37	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
38	instantiation	77, 78, 45	⊢
	: , : , :
39	instantiation	77, 46, 47	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
41	instantiation	77, 48, 49	⊢
	: , : , :
42	instantiation	50, 51, 52	⊢
	: , : , :
43	instantiation	58, 53	⊢
	: , : , :
44	instantiation	77, 67, 71	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
47	instantiation	54, 68, 55	⊢
	:
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
49	instantiation	77, 56, 57	⊢
	: , : , :
50	axiom		⊢
	proveit.logic.equality.equals_transitivity
51	instantiation	58, 59	⊢
	: , : , :
52	instantiation	60, 66	⊢
	:
53	instantiation	61, 66	⊢
	:
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
55	instantiation	62, 70, 71, 72	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
57	instantiation	77, 63, 64	⊢
	: , : , :
58	axiom		⊢
	proveit.logic.equality.substitution
59	instantiation	65, 66	⊢
	:
60	theorem		⊢
	proveit.numbers.division.frac_one_denom
61	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
63	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
64	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
65	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
66	instantiation	77, 67, 68	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
68	instantiation	69, 70, 71, 72	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
70	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
71	instantiation	77, 73, 74	⊢
	: , : , :
72	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
73	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
74	instantiation	77, 75, 76	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
76	instantiation	77, 78, 79	⊢
	: , : , :
77	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
78	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
79	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements