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	23	⊢
2	instantiation	23, 4, 5	, , ,  ⊢
	: , : , :
3	instantiation	19, 37, 38, 6, 40, 7, 8, 9, 44, 42, 26, 43	, , ,  ⊢
	: , : , : , : , : , :
4	instantiation	10, 11, 12, 13	, , ,  ⊢
	: , : , : , :
5	instantiation	30, 14	, ,  ⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
7	instantiation	45	⊢
	: , :
8	instantiation	15	⊢
	: , : , :
9	instantiation	27, 42, 43	,  ⊢
	: , :
10	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
11	instantiation	16, 37, 38, 40, 21, 20, 26, 43, 22, 42	, , ,  ⊢
	: , : , : , : , : , :
12	instantiation	17, 37, 38, 40, 20, 18, 22, 42	, , ,  ⊢
	: , : , : , : , : , : , :
13	instantiation	19, 38, 37, 20, 21, 40, 22, 42, 26, 43	, , ,  ⊢
	: , : , : , : , : , :
14	instantiation	23, 24, 25	, ,  ⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
16	theorem		⊢
	proveit.numbers.multiplication.association
17	theorem		⊢
	proveit.numbers.multiplication.rightward_commutation
18	instantiation	34, 26, 43	,  ⊢
	: , :
19	theorem		⊢
	proveit.numbers.multiplication.disassociation
20	instantiation	45	⊢
	: , :
21	instantiation	45	⊢
	: , :
22	instantiation	27, 28, 29	, ,  ⊢
	: , :
23	axiom		⊢
	proveit.logic.equality.equals_transitivity
24	instantiation	30, 31	,  ⊢
	: , : , :
25	instantiation	32, 33	, ,  ⊢
	: , :
26	assumption		⊢
27	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
28	instantiation	34, 44, 42	,  ⊢
	: , :
29	instantiation	34, 43, 44	,  ⊢
	: , :
30	axiom		⊢
	proveit.logic.equality.substitution
31	instantiation	35, 44, 42	,  ⊢
	: , :
32	theorem		⊢
	proveit.logic.equality.equals_reversal
33	instantiation	36, 37, 38, 39, 40, 41, 42, 43, 44	, ,  ⊢
	: , : , : , : , : , :
34	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
35	theorem		⊢
	proveit.numbers.multiplication.commutation
36	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
37	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
38	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
40	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
41	instantiation	45	⊢
	: , :
42	assumption		⊢
43	assumption		⊢
44	assumption		⊢
45	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq