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.merge_front
2	instantiation	5, 24, 6	⊢
	: , :
3	instantiation	7, 8	⊢
	: , :
4	instantiation	13, 9, 10	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
6	instantiation	11, 12	⊢
	:
7	theorem		⊢
	proveit.logic.equality.equals_reversal
8	instantiation	13, 14, 15	⊢
	: , : , :
9	instantiation	20, 24, 23, 57, 26, 21, 37, 36, 39	⊢
	: , : , : , : , : , :
10	instantiation	16, 39, 36, 40	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.negation.nat_closure
12	instantiation	17, 18, 19	⊢
	:
13	axiom		⊢
	proveit.logic.equality.equals_transitivity
14	instantiation	20, 24, 23, 57, 26, 21, 37, 36	⊢
	: , : , : , : , : , :
15	instantiation	22, 57, 23, 24, 25, 26, 37, 36, 27*	⊢
	: , : , : , : , : , :
16	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_31
17	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
18	instantiation	28, 53, 51	⊢
	: , :
19	instantiation	29, 42, 41, 44, 30, 31*, 32*	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.addition.disassociation
21	instantiation	33	⊢
	: , :
22	theorem		⊢
	proveit.numbers.addition.association
23	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
24	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
25	instantiation	33	⊢
	: , :
26	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
27	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
28	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
29	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
30	instantiation	34, 62	⊢
	:
31	instantiation	35, 36, 37	⊢
	: , :
32	instantiation	38, 39, 40	⊢
	: , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
34	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
35	theorem		⊢
	proveit.numbers.addition.commutation
36	instantiation	60, 43, 41	⊢
	: , : , :
37	instantiation	60, 43, 42	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
39	instantiation	60, 43, 44	⊢
	: , : , :
40	instantiation	45	⊢
	:
41	instantiation	60, 47, 46	⊢
	: , : , :
42	instantiation	60, 47, 48	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
44	instantiation	49, 50, 62	⊢
	: , : , :
45	axiom		⊢
	proveit.logic.equality.equals_reflexivity
46	instantiation	60, 52, 51	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
48	instantiation	60, 52, 53	⊢
	: , : , :
49	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
50	instantiation	54, 55	⊢
	: , :
51	instantiation	60, 56, 57	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
53	instantiation	58, 59	⊢
	:
54	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
56	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
58	theorem		⊢
	proveit.numbers.negation.int_closure
59	instantiation	60, 61, 62	⊢
	: , : , :
60	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
61	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
62	assumption		⊢
*equality replacement requirements