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	reference	28	⊢
2	modus ponens	3, 4	, ,  ⊢
3	instantiation	5, 34, 6, 35, 11, 36	⊢
	: , : , : , : , : , : , : , : , : , : , :
4	generalization	7	, ,  ⊢
5	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation_with_scalar_mult
6	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
7	instantiation	19, 8, 9	, , ,  ⊢
	: , : , :
8	instantiation	10, 11, 12, 13	, , ,  ⊢
	: , : , : , :
9	instantiation	14, 15, 16, 17	, , ,  ⊢
	: , : , : , :
10	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
11	instantiation	18, 21, 22, 37	⊢
	: , : , :
12	instantiation	19, 33, 41	,  ⊢
	: , : , :
13	instantiation	20, 21, 22, 37, 23, 38, 39	,  ⊢
	: , : , : , :
14	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
15	instantiation	24, 25, 26	, , ,  ⊢
	: , : , :
16	instantiation	27	⊢
	:
17	instantiation	28, 29	,  ⊢
	: , :
18	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
19	theorem		⊢
	proveit.logic.equality.sub_left_side_into
20	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
21	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
22	instantiation	30	⊢
	: , :
23	instantiation	30	⊢
	: , :
24	axiom		⊢
	proveit.logic.equality.equals_transitivity
25	instantiation	40, 31	,  ⊢
	: , : , :
26	instantiation	32, 33, 34, 35, 36, 37, 38, 39	, , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
27	axiom		⊢
	proveit.logic.equality.equals_reflexivity
28	theorem		⊢
	proveit.logic.equality.equals_reversal
29	instantiation	40, 41	,  ⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
31	instantiation	40, 41	,  ⊢
	: , : , :
32	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
33	instantiation	42, 48, 50	,  ⊢
	: , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
35	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
36	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
37	instantiation	43, 44	⊢
	:
38	assumption		⊢
39	assumption		⊢
40	axiom		⊢
	proveit.logic.equality.substitution
41	instantiation	45, 46, 47	,  ⊢
	: , :
42	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
43	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
44	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
45	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
46	instantiation	61, 49, 48	⊢
	: , : , :
47	instantiation	61, 49, 50	⊢
	: , : , :
48	assumption		⊢
49	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
50	instantiation	61, 51, 52	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
52	instantiation	61, 53, 54	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
54	instantiation	61, 55, 56	⊢
	: , : , :
55	instantiation	57, 58, 59	⊢
	: , :
56	assumption		⊢
57	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
58	instantiation	61, 62, 60	⊢
	: , : , :
59	instantiation	61, 62, 63	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
61	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
62	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat4