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	axiom		⊢
	proveit.numbers.summation.sum_split_last
2	reference	77	⊢
3	instantiation	6, 48, 77	⊢
	: , :
4	instantiation	7, 68, 8, 65, 9, 10*	⊢
	: , : , :
5	instantiation	49, 11, 12	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
7	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
8	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
9	instantiation	13, 71	⊢
	:
10	instantiation	14, 15, 16	⊢
	: , : , :
11	instantiation	45, 17	⊢
	: , : , :
12	instantiation	53, 80, 55, 54, 57, 56, 18, 60, 64	⊢
	: , : , : , : , : , :
13	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
14	theorem		⊢
	proveit.logic.equality.sub_right_side_into
15	instantiation	19, 64	⊢
	:
16	instantiation	20, 64, 21	⊢
	: , :
17	instantiation	22, 23, 24, 25, 26, 27	⊢
	: , : , :
18	modus ponens	28, 29	⊢
19	theorem		⊢
	proveit.numbers.addition.elim_zero_right
20	theorem		⊢
	proveit.numbers.addition.commutation
21	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
22	theorem		⊢
	proveit.core_expr_types.tuples.tuple_eq_via_elem_eq
23	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
24	instantiation	62	⊢
	: , :
25	instantiation	62	⊢
	: , :
26	instantiation	45, 30	⊢
	: , : , :
27	instantiation	66	⊢
	:
28	instantiation	31	⊢
	: , : , :
29	generalization	32	⊢
30	modus ponens	33, 34	⊢
31	theorem		⊢
	proveit.numbers.summation.summation_complex_closure
32	instantiation	78, 67, 35	,  ⊢
	: , : , :
33	instantiation	36, 37	⊢
	: , : , : , : , : , :
34	generalization	38	⊢
35	instantiation	78, 72, 39	,  ⊢
	: , : , :
36	axiom		⊢
	proveit.core_expr_types.lambda_maps.lambda_substitution
37	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
38	instantiation	45, 40	⊢
	: , : , :
39	instantiation	78, 76, 41	,  ⊢
	: , : , :
40	instantiation	45, 42	⊢
	: , : , :
41	instantiation	78, 43, 44	,  ⊢
	: , : , :
42	instantiation	45, 46	⊢
	: , : , :
43	instantiation	47, 77, 48	⊢
	: , :
44	assumption		⊢
45	axiom		⊢
	proveit.logic.equality.substitution
46	instantiation	49, 50, 51	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
48	instantiation	78, 52, 71	⊢
	: , : , :
49	axiom		⊢
	proveit.logic.equality.equals_transitivity
50	instantiation	53, 54, 55, 80, 56, 57, 60, 64, 58	⊢
	: , : , : , : , : , :
51	instantiation	59, 64, 60, 61	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
53	theorem		⊢
	proveit.numbers.addition.disassociation
54	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
56	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
57	instantiation	62	⊢
	: , :
58	instantiation	63, 64	⊢
	:
59	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
60	instantiation	78, 67, 65	⊢
	: , : , :
61	instantiation	66	⊢
	:
62	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
63	theorem		⊢
	proveit.numbers.negation.complex_closure
64	instantiation	78, 67, 68	⊢
	: , : , :
65	instantiation	69, 70, 71	⊢
	: , : , :
66	axiom		⊢
	proveit.logic.equality.equals_reflexivity
67	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
68	instantiation	78, 72, 73	⊢
	: , : , :
69	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
70	instantiation	74, 75	⊢
	: , :
71	assumption		⊢
72	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
73	instantiation	78, 76, 77	⊢
	: , : , :
74	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
75	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
76	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
77	instantiation	78, 79, 80	⊢
	: , : , :
78	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
79	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements