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	⊢
	: , : , :
1	theorem		⊢
	proveit.logic.equality.sub_left_side_into
2	instantiation	4, 52, 7, 11, 8, 5	⊢
	: , : , : , : , :
3	instantiation	6, 7, 52, 8, 9	⊢
	: , : , : , : , : , : , :
4	theorem		⊢
	proveit.logic.sets.enumeration.proper_subset_of_superset
5	instantiation	10, 52, 11, 12, 13	⊢
	: , : , :
6	theorem		⊢
	proveit.logic.sets.enumeration.leftward_permutation
7	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
8	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
9	instantiation	14	⊢
	: , :
10	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
11	instantiation	14	⊢
	: , :
12	instantiation	15, 16	⊢
	: , :
13	instantiation	19, 49, 17, 18	⊢
	: , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
15	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
16	instantiation	19, 52, 49, 20	⊢
	: , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
18	instantiation	23, 40, 24, 42, 25, 21*, 22*	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
20	instantiation	23, 42, 24, 25, 26*, 27*	⊢
	: , : , :
21	instantiation	32, 28, 29	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_4
23	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
25	instantiation	30, 31	⊢
	:
26	instantiation	32, 33, 34	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
28	instantiation	36, 35	⊢
	:
29	instantiation	37, 35, 39	⊢
	: , :
30	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
31	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
32	theorem		⊢
	proveit.logic.equality.sub_right_side_into
33	instantiation	36, 38	⊢
	:
34	instantiation	37, 38, 39	⊢
	: , :
35	instantiation	50, 41, 40	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.addition.elim_zero_right
37	theorem		⊢
	proveit.numbers.addition.commutation
38	instantiation	50, 41, 42	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
40	instantiation	50, 44, 43	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
42	instantiation	50, 44, 45	⊢
	: , : , :
43	instantiation	50, 47, 46	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
45	instantiation	50, 47, 48	⊢
	: , : , :
46	instantiation	50, 51, 49	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
48	instantiation	50, 51, 52	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
50	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
51	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
52	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements