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