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	, ,  ⊢
	: , : , :
1	reference	4	⊢
2	instantiation	4, 5, 6	, ,  ⊢
	: , : , :
3	instantiation	11, 7	⊢
	: , : , :
4	theorem		⊢
	proveit.logic.equality.sub_right_side_into
5	instantiation	8, 9, 10	, ,  ⊢
	: , :
6	instantiation	11, 12	⊢
	: , : , :
7	instantiation	37, 38	⊢
	: , :
8	theorem		⊢
	proveit.logic.equality.lhs_via_equality
9	instantiation	13, 14, 15	, ,  ⊢
	: , :
10	instantiation	16, 38	⊢
	: , : , : , : , :
11	theorem		⊢
	proveit.core_expr_types.tuples.merge_extension
12	instantiation	37, 38	⊢
	: , :
13	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
14	instantiation	17, 18	, ,  ⊢
	: , :
15	instantiation	19, 38, 21, 23, 22, 24	,  ⊢
	: , : , : , : , :
16	axiom		⊢
	proveit.core_expr_types.tuples.tuple_eq_def
17	assumption		⊢
18	instantiation	20, 21, 38, 36, 22, 23, 24	,  ⊢
	: , : , : , : , : , :
19	theorem		⊢
	proveit.logic.booleans.conjunction.any_from_and
20	theorem		⊢
	proveit.logic.booleans.conjunction.some_from_and
21	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
22	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
23	instantiation	30, 38	⊢
	: , :
24	instantiation	25, 31, 26, 27, 28, 29	,  ⊢
	: , : , : , :
25	theorem		⊢
	proveit.logic.equality.sub_in_right_operands_via_tuple
26	instantiation	30, 31	⊢
	: , :
27	instantiation	32, 38	⊢
	: , : , :
28	assumption		⊢
29	instantiation	33, 34	⊢
	: , : , :
30	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
31	instantiation	35, 38, 36	⊢
	: , :
32	theorem		⊢
	proveit.core_expr_types.tuples.extended_range_from1_len_typical_eq
33	axiom		⊢
	proveit.core_expr_types.tuples.range_extension_def
34	instantiation	37, 38	⊢
	: , :
35	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
36	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
37	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_is_nat
38	instantiation	39, 40, 41	⊢
	: , : , :
39	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
40	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
41	assumption		⊢