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	theorem		⊢
	proveit.core_expr_types.tuples.range_len_is_nat
2	instantiation	52, 3, 4	⊢
	: , : , :
3	instantiation	5, 6	⊢
	:
4	instantiation	28, 7, 8, 9	⊢
	: , : , : , :
5	theorem		⊢
	proveit.numbers.negation.nat_closure
6	instantiation	10, 11, 12	⊢
	:
7	instantiation	33, 34, 60, 35*	⊢
	: , :
8	instantiation	32	⊢
	:
9	instantiation	13, 14	⊢
	: , :
10	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
11	instantiation	15, 62, 77	⊢
	: , :
12	instantiation	16, 47, 65, 56, 17, 18*, 19*	⊢
	: , : , :
13	theorem		⊢
	proveit.logic.equality.equals_reversal
14	instantiation	20, 21, 22	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
16	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
17	instantiation	23, 76	⊢
	:
18	instantiation	59, 60, 34	⊢
	: , :
19	instantiation	24, 49, 25	⊢
	: , :
20	axiom		⊢
	proveit.logic.equality.equals_transitivity
21	instantiation	26, 27	⊢
	: , : , :
22	instantiation	28, 29, 30, 31	⊢
	: , : , : , :
23	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
24	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
25	instantiation	32	⊢
	:
26	axiom		⊢
	proveit.logic.equality.substitution
27	instantiation	33, 34, 67, 35*	⊢
	: , :
28	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
29	instantiation	36, 80, 85, 37, 38, 49, 61, 60	⊢
	: , : , : , : , : , :
30	instantiation	39, 43, 40, 45, 41, 49, 61, 60	⊢
	: , : , : , :
31	instantiation	42, 80, 85, 43, 44, 45, 49, 61, 60, 46*	⊢
	: , : , : , : , : , :
32	axiom		⊢
	proveit.logic.equality.equals_reflexivity
33	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
34	instantiation	83, 73, 47	⊢
	: , : , :
35	instantiation	48, 49	⊢
	:
36	theorem		⊢
	proveit.numbers.addition.disassociation
37	instantiation	51	⊢
	: , :
38	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
39	theorem		⊢
	proveit.numbers.addition.elim_zero_any
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
41	instantiation	50	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.addition.association
43	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
44	instantiation	51	⊢
	: , :
45	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
46	instantiation	52, 53, 54	⊢
	: , : , :
47	instantiation	83, 78, 55	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.negation.double_negation
49	instantiation	83, 73, 56	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
51	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
52	theorem		⊢
	proveit.logic.equality.sub_right_side_into
53	instantiation	57, 60, 67, 58	⊢
	: , : , :
54	instantiation	59, 60, 61	⊢
	: , :
55	instantiation	83, 81, 62	⊢
	: , : , :
56	instantiation	63, 64, 76	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
58	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
59	theorem		⊢
	proveit.numbers.addition.commutation
60	instantiation	83, 73, 65	⊢
	: , : , :
61	instantiation	66, 67	⊢
	:
62	instantiation	68, 69	⊢
	:
63	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
64	instantiation	70, 71	⊢
	: , :
65	instantiation	83, 78, 72	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.negation.complex_closure
67	instantiation	83, 73, 74	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.negation.int_closure
69	instantiation	83, 75, 76	⊢
	: , : , :
70	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
71	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
72	instantiation	83, 81, 77	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
74	instantiation	83, 78, 79	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
76	assumption		⊢
77	instantiation	83, 84, 80	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
79	instantiation	83, 81, 82	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
81	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
82	instantiation	83, 84, 85	⊢
	: , : , :
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.nat2
*equality replacement requirements