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	modus ponens	1, 2	, ,  ⊢
1	instantiation	3, 32, 4, 33, 9, 34	⊢
	: , : , : , : , : , : , : , : , : , : , :
2	generalization	5	, ,  ⊢
3	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation_with_scalar_mult
4	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
5	instantiation	17, 6, 7	, , ,  ⊢
	: , : , :
6	instantiation	8, 9, 10, 11	, , ,  ⊢
	: , : , : , :
7	instantiation	12, 13, 14, 15	, , ,  ⊢
	: , : , : , :
8	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
9	instantiation	16, 19, 20, 35	⊢
	: , : , :
10	instantiation	17, 31, 39	,  ⊢
	: , : , :
11	instantiation	18, 19, 20, 35, 21, 36, 37	,  ⊢
	: , : , : , :
12	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
13	instantiation	22, 23, 24	, , ,  ⊢
	: , : , :
14	instantiation	25	⊢
	:
15	instantiation	26, 27	,  ⊢
	: , :
16	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
17	theorem		⊢
	proveit.logic.equality.sub_left_side_into
18	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
19	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
20	instantiation	28	⊢
	: , :
21	instantiation	28	⊢
	: , :
22	axiom		⊢
	proveit.logic.equality.equals_transitivity
23	instantiation	38, 29	,  ⊢
	: , : , :
24	instantiation	30, 31, 32, 33, 34, 35, 36, 37	, , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
25	axiom		⊢
	proveit.logic.equality.equals_reflexivity
26	theorem		⊢
	proveit.logic.equality.equals_reversal
27	instantiation	38, 39	,  ⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
29	instantiation	38, 39	,  ⊢
	: , : , :
30	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
31	instantiation	40, 46, 48	,  ⊢
	: , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
33	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
34	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
35	instantiation	41, 42	⊢
	:
36	assumption		⊢
37	assumption		⊢
38	axiom		⊢
	proveit.logic.equality.substitution
39	instantiation	43, 44, 45	,  ⊢
	: , :
40	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
41	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
42	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
43	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
44	instantiation	59, 47, 46	⊢
	: , : , :
45	instantiation	59, 47, 48	⊢
	: , : , :
46	assumption		⊢
47	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
48	instantiation	59, 49, 50	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
50	instantiation	59, 51, 52	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
52	instantiation	59, 53, 54	⊢
	: , : , :
53	instantiation	55, 56, 57	⊢
	: , :
54	assumption		⊢
55	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
56	instantiation	59, 60, 58	⊢
	: , : , :
57	instantiation	59, 60, 61	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
59	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
60	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat4