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*	⊢
	: , :
1	theorem		⊢
	proveit.numbers.number_sets.integers.interval_cardinality
2	reference	50	⊢
3	reference	52	⊢
4	instantiation	6, 42, 7, 41, 8, 9*, 39*	⊢
	: , : , :
5	instantiation	10, 11, 12, 40, 13, 14, 38, 15, 16, 17*	⊢
	: , : , : , : , : , :
6	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
7	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
8	instantiation	18, 53	⊢
	:
9	instantiation	19, 20, 21	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.addition.association
11	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
12	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
13	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
14	instantiation	22	⊢
	: , :
15	instantiation	23, 37	⊢
	:
16	instantiation	55, 43, 24	⊢
	: , : , :
17	instantiation	25, 26, 27	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
19	theorem		⊢
	proveit.logic.equality.sub_right_side_into
20	instantiation	28, 37	⊢
	:
21	instantiation	29, 37, 30	⊢
	: , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
23	theorem		⊢
	proveit.numbers.negation.complex_closure
24	instantiation	55, 47, 31	⊢
	: , : , :
25	axiom		⊢
	proveit.logic.equality.equals_transitivity
26	instantiation	32, 33	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.add_5_1
28	theorem		⊢
	proveit.numbers.addition.elim_zero_right
29	theorem		⊢
	proveit.numbers.addition.commutation
30	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
31	instantiation	55, 51, 34	⊢
	: , : , :
32	axiom		⊢
	proveit.logic.equality.substitution
33	instantiation	35, 36, 37, 38, 39	⊢
	: , : , :
34	instantiation	55, 56, 40	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
36	instantiation	55, 43, 41	⊢
	: , : , :
37	instantiation	55, 43, 42	⊢
	: , : , :
38	instantiation	55, 43, 44	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.add_5_3
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
41	instantiation	55, 47, 45	⊢
	: , : , :
42	instantiation	55, 47, 46	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
44	instantiation	55, 47, 48	⊢
	: , : , :
45	instantiation	55, 51, 49	⊢
	: , : , :
46	instantiation	55, 51, 50	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
48	instantiation	55, 51, 52	⊢
	: , : , :
49	instantiation	55, 56, 53	⊢
	: , : , :
50	instantiation	55, 56, 54	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
52	instantiation	55, 56, 57	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
54	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
55	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
56	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat8
*equality replacement requirements