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	⊢
	: , : , : , :
1	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
2	instantiation	5	⊢
	: , : , :
3	instantiation	6	⊢
	:
4	instantiation	7, 8	⊢
	: , :
5	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3
6	axiom		⊢
	proveit.logic.equality.equals_reflexivity
7	theorem		⊢
	proveit.logic.equality.equals_reversal
8	instantiation	9, 10, 11	⊢
	: , : , :
9	theorem		⊢
	proveit.logic.equality.sub_right_side_into
10	instantiation	12, 13	⊢
	: , : , :
11	instantiation	30, 14, 15	⊢
	: , : , :
12	theorem		⊢
	proveit.core_expr_types.tuples.range_len
13	instantiation	54, 16, 17	⊢
	: , : , :
14	instantiation	38, 43	⊢
	: , : , :
15	instantiation	18, 24, 56, 47, 26, 19, 46, 20, 21, 22*	⊢
	: , : , : , : , : , :
16	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
17	instantiation	23, 56, 24, 25, 26, 27, 47, 28	⊢
	: , : , : , : , :
18	theorem		⊢
	proveit.numbers.addition.association
19	instantiation	33	⊢
	: , :
20	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
21	instantiation	54, 48, 29	⊢
	: , : , :
22	instantiation	30, 31, 32	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
24	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
25	instantiation	33	⊢
	: , :
26	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
27	instantiation	34, 35, 36	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
29	instantiation	54, 50, 37	⊢
	: , : , :
30	axiom		⊢
	proveit.logic.equality.equals_transitivity
31	instantiation	38, 39	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
33	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
34	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
35	instantiation	40, 41	⊢
	: , :
36	instantiation	42, 43	⊢
	: , :
37	instantiation	54, 52, 44	⊢
	: , : , :
38	axiom		⊢
	proveit.logic.equality.substitution
39	instantiation	45, 46	⊢
	:
40	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
41	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.zero_set_within_nat
42	theorem		⊢
	proveit.logic.sets.enumeration.fold_singleton
43	theorem		⊢
	proveit.numbers.negation.negated_zero
44	instantiation	54, 55, 47	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.addition.elim_zero_right
46	instantiation	54, 48, 49	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
48	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
49	instantiation	54, 50, 51	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
51	instantiation	54, 52, 53	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
53	instantiation	54, 55, 56	⊢
	: , : , :
54	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
55	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
56	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements