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.numbers.division.distribute_frac_through_sum
2	instantiation	10, 23, 46, 11, 12	⊢
	: , :
3	instantiation	36, 37, 13	⊢
	: , : , :
4	instantiation	14, 15, 16, 17	⊢
	: , : , : , :
5	assumption		⊢
6	assumption		⊢
7	assumption		⊢
8	assumption		⊢
9	assumption		⊢
10	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure
11	instantiation	18, 26, 19	⊢
	:
12	instantiation	35, 76, 49	⊢
	: , : , :
13	instantiation	36, 20, 21	⊢
	: , : , :
14	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
15	instantiation	22, 23, 24, 25, 47, 26, 27, 28*	⊢
	: , : , : , :
16	instantiation	29, 30, 62	⊢
	: , :
17	instantiation	31, 32	⊢
	: , :
18	theorem		⊢
	proveit.numbers.number_sets.integers.nonzero_nat_is_natural_pos
19	instantiation	35, 33, 48	⊢
	: , : , :
20	instantiation	34, 51, 71, 52, 53, 61, 62	⊢
	: , : , : , : , : , : , :
21	instantiation	50, 83, 71, 51, 53, 52, 62, 61, 54*	⊢
	: , : , : , : , : , :
22	theorem		⊢
	proveit.core_expr_types.tuples.general_len
23	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
24	instantiation	58	⊢
	: , : , :
25	instantiation	58	⊢
	: , : , :
26	instantiation	35, 83, 48	⊢
	: , : , :
27	instantiation	35, 57, 49	⊢
	: , : , :
28	instantiation	36, 37, 38	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.addition.commutation
30	instantiation	81, 68, 39	⊢
	: , : , :
31	theorem		⊢
	proveit.logic.equality.equals_reversal
32	instantiation	40, 41	⊢
	: , :
33	instantiation	42, 43	⊢
	:
34	theorem		⊢
	proveit.numbers.addition.leftward_commutation
35	theorem		⊢
	proveit.logic.equality.sub_left_side_into
36	axiom		⊢
	proveit.logic.equality.equals_transitivity
37	instantiation	44, 45, 46, 47, 48, 49	⊢
	: , : , : , :
38	instantiation	50, 51, 71, 83, 52, 53, 61, 62, 54*	⊢
	: , : , : , : , : , :
39	instantiation	81, 72, 55	⊢
	: , : , :
40	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
41	instantiation	56, 57, 71	⊢
	: , :
42	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
43	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
44	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
46	instantiation	58	⊢
	: , : , :
47	instantiation	58	⊢
	: , : , :
48	instantiation	59, 61, 63	⊢
	: , : , :
49	instantiation	60, 61, 62, 63	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.addition.association
51	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
52	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
53	instantiation	64	⊢
	: , :
54	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
55	instantiation	81, 77, 65	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
57	instantiation	81, 66, 76	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
59	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
60	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
61	instantiation	81, 68, 67	⊢
	: , : , :
62	instantiation	81, 68, 69	⊢
	: , : , :
63	instantiation	70	⊢
	:
64	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
65	instantiation	81, 82, 71	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
67	instantiation	81, 72, 73	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
69	instantiation	74, 75, 76	⊢
	: , : , :
70	axiom		⊢
	proveit.logic.equality.equals_reflexivity
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
72	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
73	instantiation	81, 77, 78	⊢
	: , : , :
74	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
75	instantiation	79, 80	⊢
	: , :
76	assumption		⊢
77	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
78	instantiation	81, 82, 83	⊢
	: , : , :
79	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
80	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
81	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
82	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
83	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements