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.logic.sets.inclusion.unfold_proper_subset
2	instantiation	3, 4, 5	⊢
	: , : , :
3	theorem		⊢
	proveit.logic.equality.sub_left_side_into
4	instantiation	6, 54, 9, 13, 10, 7	⊢
	: , : , : , : , :
5	instantiation	8, 9, 54, 10, 11	⊢
	: , : , : , : , : , : , :
6	theorem		⊢
	proveit.logic.sets.enumeration.proper_subset_of_superset
7	instantiation	12, 54, 13, 14, 15	⊢
	: , : , :
8	theorem		⊢
	proveit.logic.sets.enumeration.leftward_permutation
9	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
10	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
11	instantiation	16	⊢
	: , :
12	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
13	instantiation	16	⊢
	: , :
14	instantiation	17, 18	⊢
	: , :
15	instantiation	21, 51, 19, 20	⊢
	: , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
17	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
18	instantiation	21, 54, 51, 22	⊢
	: , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
20	instantiation	25, 42, 26, 44, 27, 23*, 24*	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
22	instantiation	25, 44, 26, 27, 28*, 29*	⊢
	: , : , :
23	instantiation	34, 30, 31	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_4
25	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
27	instantiation	32, 33	⊢
	:
28	instantiation	34, 35, 36	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
30	instantiation	38, 37	⊢
	:
31	instantiation	39, 37, 41	⊢
	: , :
32	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
33	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
34	theorem		⊢
	proveit.logic.equality.sub_right_side_into
35	instantiation	38, 40	⊢
	:
36	instantiation	39, 40, 41	⊢
	: , :
37	instantiation	52, 43, 42	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.addition.elim_zero_right
39	theorem		⊢
	proveit.numbers.addition.commutation
40	instantiation	52, 43, 44	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
42	instantiation	52, 46, 45	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
44	instantiation	52, 46, 47	⊢
	: , : , :
45	instantiation	52, 49, 48	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
47	instantiation	52, 49, 50	⊢
	: , : , :
48	instantiation	52, 53, 51	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
50	instantiation	52, 53, 54	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
52	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
53	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
54	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements