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*	⊢
	: , : , :
1	theorem		⊢
	proveit.core_expr_types.tuples.partition_front
2	instantiation	5, 18, 6	⊢
	: , :
3	instantiation	9, 7, 8	⊢
	: , : , :
4	instantiation	9, 10, 11	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
6	instantiation	12, 13	⊢
	:
7	instantiation	17, 18, 19, 55, 20, 21, 35, 34	⊢
	: , : , : , : , : , :
8	instantiation	14, 55, 19, 18, 15, 20, 35, 34, 16*	⊢
	: , : , : , : , : , :
9	axiom		⊢
	proveit.logic.equality.equals_transitivity
10	instantiation	17, 18, 19, 55, 20, 21, 35, 34, 37	⊢
	: , : , : , : , : , :
11	instantiation	22, 37, 34, 38	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.negation.nat_closure
13	instantiation	23, 24, 25	⊢
	:
14	theorem		⊢
	proveit.numbers.addition.association
15	instantiation	26	⊢
	: , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
17	theorem		⊢
	proveit.numbers.addition.disassociation
18	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
19	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
20	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
21	instantiation	26	⊢
	: , :
22	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_31
23	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
24	instantiation	27, 51, 49	⊢
	: , :
25	instantiation	28, 40, 39, 42, 29, 30*, 31*	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
27	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
28	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
29	instantiation	32, 60	⊢
	:
30	instantiation	33, 34, 35	⊢
	: , :
31	instantiation	36, 37, 38	⊢
	: , :
32	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
33	theorem		⊢
	proveit.numbers.addition.commutation
34	instantiation	58, 41, 39	⊢
	: , : , :
35	instantiation	58, 41, 40	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
37	instantiation	58, 41, 42	⊢
	: , : , :
38	instantiation	43	⊢
	:
39	instantiation	58, 45, 44	⊢
	: , : , :
40	instantiation	58, 45, 46	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
42	instantiation	47, 48, 60	⊢
	: , : , :
43	axiom		⊢
	proveit.logic.equality.equals_reflexivity
44	instantiation	58, 50, 49	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
46	instantiation	58, 50, 51	⊢
	: , : , :
47	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
48	instantiation	52, 53	⊢
	: , :
49	instantiation	58, 54, 55	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
51	instantiation	56, 57	⊢
	:
52	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
56	theorem		⊢
	proveit.numbers.negation.int_closure
57	instantiation	58, 59, 60	⊢
	: , : , :
58	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
59	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
60	assumption		⊢
*equality replacement requirements