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	⊢
	: , : , :
1	theorem		⊢
	proveit.core_expr_types.tuples.tuple_eq_via_elem_eq
2	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
3	instantiation	29	⊢
	: , :
4	instantiation	29	⊢
	: , :
5	instantiation	15, 7	⊢
	: , : , :
6	instantiation	33	⊢
	:
7	modus ponens	8, 9	⊢
8	instantiation	10, 11	⊢
	: , : , : , : , : , :
9	generalization	12	⊢
10	axiom		⊢
	proveit.core_expr_types.lambda_maps.lambda_substitution
11	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
12	instantiation	15, 13	⊢
	: , : , :
13	instantiation	15, 14	⊢
	: , : , :
14	instantiation	15, 16	⊢
	: , : , :
15	axiom		⊢
	proveit.logic.equality.substitution
16	instantiation	17, 18, 19	⊢
	: , : , :
17	axiom		⊢
	proveit.logic.equality.equals_transitivity
18	instantiation	20, 21, 22, 47, 23, 24, 27, 31, 25	⊢
	: , : , : , : , : , :
19	instantiation	26, 31, 27, 28	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.addition.disassociation
21	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
22	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
23	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
24	instantiation	29	⊢
	: , :
25	instantiation	30, 31	⊢
	:
26	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
27	instantiation	45, 34, 32	⊢
	: , : , :
28	instantiation	33	⊢
	:
29	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
30	theorem		⊢
	proveit.numbers.negation.complex_closure
31	instantiation	45, 34, 35	⊢
	: , : , :
32	instantiation	36, 37, 38	⊢
	: , : , :
33	axiom		⊢
	proveit.logic.equality.equals_reflexivity
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
35	instantiation	45, 39, 40	⊢
	: , : , :
36	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
37	instantiation	41, 42	⊢
	: , :
38	assumption		⊢
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
40	instantiation	45, 43, 44	⊢
	: , : , :
41	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
43	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
44	instantiation	45, 46, 47	⊢
	: , : , :
45	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat1