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