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	, , , , ,  ⊢
	: , :
1	reference	33	⊢
2	instantiation	3, 4, 5, 6, 7, 8, 9, 10, 11	, , , , ,  ⊢
	: , : , :
3	theorem		⊢
	proveit.numbers.division.distribute_frac_through_sum
4	instantiation	12, 25, 48, 13, 14	⊢
	: , :
5	instantiation	38, 39, 15	⊢
	: , : , :
6	instantiation	16, 17, 18, 19	⊢
	: , : , : , :
7	assumption		⊢
8	assumption		⊢
9	assumption		⊢
10	assumption		⊢
11	assumption		⊢
12	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure
13	instantiation	20, 28, 21	⊢
	:
14	instantiation	37, 78, 51	⊢
	: , : , :
15	instantiation	38, 22, 23	⊢
	: , : , :
16	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
17	instantiation	24, 25, 26, 27, 49, 28, 29, 30*	⊢
	: , : , : , :
18	instantiation	31, 32, 64	⊢
	: , :
19	instantiation	33, 34	⊢
	: , :
20	theorem		⊢
	proveit.numbers.number_sets.integers.nonzero_nat_is_natural_pos
21	instantiation	37, 35, 50	⊢
	: , : , :
22	instantiation	36, 53, 73, 54, 55, 63, 64	⊢
	: , : , : , : , : , : , :
23	instantiation	52, 85, 73, 53, 55, 54, 64, 63, 56*	⊢
	: , : , : , : , : , :
24	theorem		⊢
	proveit.core_expr_types.tuples.general_len
25	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
26	instantiation	60	⊢
	: , : , :
27	instantiation	60	⊢
	: , : , :
28	instantiation	37, 85, 50	⊢
	: , : , :
29	instantiation	37, 59, 51	⊢
	: , : , :
30	instantiation	38, 39, 40	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.addition.commutation
32	instantiation	83, 70, 41	⊢
	: , : , :
33	theorem		⊢
	proveit.logic.equality.equals_reversal
34	instantiation	42, 43	⊢
	: , :
35	instantiation	44, 45	⊢
	:
36	theorem		⊢
	proveit.numbers.addition.leftward_commutation
37	theorem		⊢
	proveit.logic.equality.sub_left_side_into
38	axiom		⊢
	proveit.logic.equality.equals_transitivity
39	instantiation	46, 47, 48, 49, 50, 51	⊢
	: , : , : , :
40	instantiation	52, 53, 73, 85, 54, 55, 63, 64, 56*	⊢
	: , : , : , : , : , :
41	instantiation	83, 74, 57	⊢
	: , : , :
42	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
43	instantiation	58, 59, 73	⊢
	: , :
44	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
45	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
46	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
48	instantiation	60	⊢
	: , : , :
49	instantiation	60	⊢
	: , : , :
50	instantiation	61, 63, 65	⊢
	: , : , :
51	instantiation	62, 63, 64, 65	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.addition.association
53	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
54	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
55	instantiation	66	⊢
	: , :
56	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
57	instantiation	83, 79, 67	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
59	instantiation	83, 68, 78	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
61	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
62	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
63	instantiation	83, 70, 69	⊢
	: , : , :
64	instantiation	83, 70, 71	⊢
	: , : , :
65	instantiation	72	⊢
	:
66	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
67	instantiation	83, 84, 73	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
69	instantiation	83, 74, 75	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
71	instantiation	76, 77, 78	⊢
	: , : , :
72	axiom		⊢
	proveit.logic.equality.equals_reflexivity
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
74	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
75	instantiation	83, 79, 80	⊢
	: , : , :
76	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
77	instantiation	81, 82	⊢
	: , :
78	assumption		⊢
79	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
80	instantiation	83, 84, 85	⊢
	: , : , :
81	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
82	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
83	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
84	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
85	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements