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	⊢
	: , :
1	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_all
2	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
3	instantiation	8	⊢
	: , : , : , :
4	instantiation	84	⊢
	:
5	reference	28	⊢
6	modus ponens	9, 10	⊢
7	instantiation	84	⊢
	:
8	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
9	instantiation	11, 95, 96, 12	⊢
	: , : , : , :
10	generalization	13	⊢
11	theorem		⊢
	proveit.logic.booleans.conjunction.conjunction_from_quantification
12	instantiation	14, 15, 66, 81, 16, 17*, 18*	⊢
	: , : , :
13	instantiation	38, 19	,  ⊢
	: , :
14	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
15	instantiation	108, 92, 20	⊢
	: , : , :
16	instantiation	21, 110	⊢
	:
17	instantiation	25, 22, 23, 24	⊢
	: , : , : , :
18	instantiation	25, 26, 27, 28	⊢
	: , : , : , :
19	instantiation	60, 29, 30	,  ⊢
	: , : , :
20	instantiation	108, 100, 31	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
22	instantiation	60, 32, 33	⊢
	: , : , :
23	instantiation	34, 64, 73, 74, 35	⊢
	: , : , :
24	instantiation	84	⊢
	:
25	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
26	instantiation	60, 36, 37	⊢
	: , : , :
27	instantiation	84	⊢
	:
28	instantiation	38, 39	⊢
	: , :
29	instantiation	67, 68, 40, 97, 70, 41, 44, 42, 73, 58	,  ⊢
	: , : , : , : , : , :
30	instantiation	43, 97, 68, 70, 44, 58, 73	,  ⊢
	: , : , : , : , : , : , : , :
31	instantiation	101, 102, 88	⊢
	: , :
32	instantiation	67, 97, 107, 68, 50, 70, 58, 71	⊢
	: , : , : , : , : , :
33	instantiation	60, 45, 46	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
35	instantiation	47, 48, 49	⊢
	: , : , :
36	instantiation	67, 97, 107, 68, 50, 70, 73, 71, 58	⊢
	: , : , : , : , : , :
37	instantiation	72, 73, 58, 75	⊢
	: , : , :
38	theorem		⊢
	proveit.logic.equality.equals_reversal
39	instantiation	51, 58	⊢
	:
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
41	instantiation	52	⊢
	: , : , :
42	instantiation	53, 58	⊢
	:
43	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general_rev
44	instantiation	108, 82, 54	,  ⊢
	: , : , :
45	instantiation	55, 97, 68, 70, 58, 71	⊢
	: , : , : , : , : , : , :
46	instantiation	56, 68, 107, 97, 70, 57, 58, 71, 59*	⊢
	: , : , : , : , : , :
47	theorem		⊢
	proveit.logic.equality.sub_right_side_into
48	instantiation	60, 61, 62	⊢
	: , : , :
49	instantiation	63, 73, 64	⊢
	: , :
50	instantiation	79	⊢
	: , :
51	theorem		⊢
	proveit.numbers.addition.elim_zero_left
52	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
53	theorem		⊢
	proveit.numbers.negation.complex_closure
54	instantiation	108, 92, 65	,  ⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.addition.leftward_commutation
56	theorem		⊢
	proveit.numbers.addition.association
57	instantiation	79	⊢
	: , :
58	instantiation	108, 82, 66	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
60	axiom		⊢
	proveit.logic.equality.equals_transitivity
61	instantiation	67, 97, 107, 68, 69, 70, 73, 71, 74	⊢
	: , : , : , : , : , :
62	instantiation	72, 73, 74, 75	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.addition.commutation
64	instantiation	108, 82, 76	⊢
	: , : , :
65	instantiation	108, 100, 77	,  ⊢
	: , : , :
66	instantiation	108, 92, 78	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.addition.disassociation
68	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
69	instantiation	79	⊢
	: , :
70	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
71	instantiation	108, 82, 80	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
73	instantiation	108, 82, 81	⊢
	: , : , :
74	instantiation	108, 82, 83	⊢
	: , : , :
75	instantiation	84	⊢
	:
76	instantiation	108, 92, 85	⊢
	: , : , :
77	instantiation	108, 86, 87	,  ⊢
	: , : , :
78	instantiation	108, 100, 88	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
80	instantiation	108, 92, 89	⊢
	: , : , :
81	instantiation	90, 91, 110	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
83	instantiation	108, 92, 93	⊢
	: , : , :
84	axiom		⊢
	proveit.logic.equality.equals_reflexivity
85	instantiation	108, 100, 95	⊢
	: , : , :
86	instantiation	94, 95, 96	⊢
	: , :
87	assumption		⊢
88	instantiation	108, 106, 97	⊢
	: , : , :
89	instantiation	108, 100, 102	⊢
	: , : , :
90	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
91	instantiation	98, 99	⊢
	: , :
92	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
93	instantiation	108, 100, 103	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
95	instantiation	101, 102, 103	⊢
	: , :
96	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
97	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
98	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
99	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
100	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
101	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
102	instantiation	104, 105	⊢
	:
103	instantiation	108, 106, 107	⊢
	: , : , :
104	theorem		⊢
	proveit.numbers.negation.int_closure
105	instantiation	108, 109, 110	⊢
	: , : , :
106	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
107	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
108	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
109	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
110	assumption		⊢
*equality replacement requirements