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	, , , ,  ⊢
	: , :
1	theorem		⊢
	proveit.numbers.absolute_value.generalized_triangle_inequality
2	instantiation	9, 57, 83, 59, 63, 66, 10	⊢
	: , : , : , : , :
3	reference	13	⊢
4	instantiation	11, 12, 13, 14	⊢
	: , : , : , :
5	assumption		⊢
6	assumption		⊢
7	assumption		⊢
8	assumption		⊢
9	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
10	instantiation	15, 16	⊢
	:
11	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
12	instantiation	17, 18, 19, 20, 37, 21, 22, 23*	⊢
	: , : , : , :
13	instantiation	24, 25, 50	⊢
	: , :
14	instantiation	26, 27	⊢
	: , :
15	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
16	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
17	theorem		⊢
	proveit.core_expr_types.tuples.general_len
18	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
19	instantiation	44	⊢
	: , : , : , :
20	instantiation	44	⊢
	: , : , : , :
21	instantiation	28, 83, 38	⊢
	: , : , :
22	instantiation	28, 66, 39	⊢
	: , : , :
23	instantiation	70, 29, 30	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.addition.commutation
25	instantiation	81, 68, 31	⊢
	: , : , :
26	theorem		⊢
	proveit.logic.equality.equals_reversal
27	instantiation	32, 33	⊢
	: , :
28	theorem		⊢
	proveit.logic.equality.sub_left_side_into
29	instantiation	34, 35, 36, 37, 38, 39	⊢
	: , : , : , :
30	instantiation	70, 40, 41	⊢
	: , : , :
31	instantiation	81, 75, 42	⊢
	: , : , :
32	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
33	instantiation	43, 66, 63	⊢
	: , :
34	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
35	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
36	instantiation	44	⊢
	: , : , : , :
37	instantiation	44	⊢
	: , : , : , :
38	instantiation	45, 61, 47	⊢
	: , : , :
39	instantiation	46, 61, 50, 47	⊢
	: , : , :
40	instantiation	48, 58, 83, 57, 60, 59, 61, 50	⊢
	: , : , : , : , : , : , :
41	instantiation	56, 57, 63, 83, 59, 49, 61, 50, 51*	⊢
	: , : , : , : , : , :
42	instantiation	81, 79, 52	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
44	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
45	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
46	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
47	instantiation	53	⊢
	:
48	theorem		⊢
	proveit.numbers.addition.leftward_commutation
49	instantiation	54	⊢
	: , : , :
50	instantiation	81, 68, 55	⊢
	: , : , :
51	instantiation	56, 57, 58, 83, 59, 60, 61, 62*	⊢
	: , : , : , : , : , :
52	instantiation	81, 82, 63	⊢
	: , : , :
53	axiom		⊢
	proveit.logic.equality.equals_reflexivity
54	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
55	instantiation	64, 65, 66	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.addition.association
57	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
58	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
59	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
60	instantiation	67	⊢
	: , :
61	instantiation	81, 68, 69	⊢
	: , : , :
62	instantiation	70, 71, 72	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
64	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
65	instantiation	73, 74	⊢
	: , :
66	assumption		⊢
67	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
68	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
69	instantiation	81, 75, 76	⊢
	: , : , :
70	axiom		⊢
	proveit.logic.equality.equals_transitivity
71	instantiation	77, 78	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
73	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
74	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_within_real
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
76	instantiation	81, 79, 80	⊢
	: , : , :
77	axiom		⊢
	proveit.logic.equality.substitution
78	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
79	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
80	instantiation	81, 82, 83	⊢
	: , : , :
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