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	7	⊢
2	instantiation	3, 4, 5	, ,  ⊢
	: , : , :
3	axiom		⊢
	proveit.logic.equality.equals_transitivity
4	instantiation	11, 6	, ,  ⊢
	: , :
5	instantiation	7, 8	,  ⊢
	: , : , :
6	modus ponens	9, 10	, ,  ⊢
7	axiom		⊢
	proveit.logic.equality.substitution
8	instantiation	11, 12	,  ⊢
	: , :
9	instantiation	13, 21, 23, 14	⊢
	: , : , : , : , : , : , :
10	modus ponens	15, 17	,  ⊢
11	theorem		⊢
	proveit.logic.equality.equals_reversal
12	modus ponens	16, 17	,  ⊢
13	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum
14	assumption		⊢
15	instantiation	18, 21, 23	⊢
	: , : , : , : , : , :
16	instantiation	19, 20, 21, 22, 23, 24	⊢
	: , : , : , : , : , : , : , : , : , :
17	generalization	25	,  ⊢
18	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
19	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation
20	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
21	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
22	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
23	instantiation	26, 49, 28, 29	⊢
	: , : , :
24	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
25	instantiation	27, 49, 28, 29, 30, 31, 32	, ,  ⊢
	: , : , : , :
26	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
27	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
28	instantiation	35	⊢
	: , :
29	instantiation	33, 34	⊢
	:
30	instantiation	35	⊢
	: , :
31	assumption		⊢
32	instantiation	36, 37	,  ⊢
	:
33	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
34	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
35	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
36	assumption		⊢
37	instantiation	38, 39, 40	⊢
	:
38	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
39	instantiation	55, 41, 53	⊢
	: , : , :
40	instantiation	42, 43	⊢
	: , :
41	instantiation	44, 51, 52	⊢
	: , :
42	theorem		⊢
	proveit.numbers.ordering.relax_less
43	instantiation	45, 46, 47	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
45	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
46	instantiation	48, 49	⊢
	:
47	instantiation	50, 51, 52, 53	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
49	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
50	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
51	instantiation	55, 56, 54	⊢
	: , : , :
52	instantiation	55, 56, 57	⊢
	: , : , :
53	assumption		⊢
54	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
55	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
56	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat4