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, 8, 9, 10, 11, 12	⊢
	: , : , : , : , : , : , : , : , : , :
6	generalization	13	,  ⊢
7	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation
8	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
9	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
10	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
11	instantiation	14, 37, 16, 17	⊢
	: , : , :
12	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
13	instantiation	15, 37, 16, 17, 18, 19, 20	, ,  ⊢
	: , : , : , :
14	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
15	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
16	instantiation	23	⊢
	: , :
17	instantiation	21, 22	⊢
	:
18	instantiation	23	⊢
	: , :
19	assumption		⊢
20	instantiation	24, 25	,  ⊢
	:
21	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
23	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
24	assumption		⊢
25	instantiation	26, 27, 28	⊢
	:
26	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
27	instantiation	43, 29, 41	⊢
	: , : , :
28	instantiation	30, 31	⊢
	: , :
29	instantiation	32, 39, 40	⊢
	: , :
30	theorem		⊢
	proveit.numbers.ordering.relax_less
31	instantiation	33, 34, 35	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
33	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
34	instantiation	36, 37	⊢
	:
35	instantiation	38, 39, 40, 41	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
37	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
38	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
39	instantiation	43, 44, 42	⊢
	: , : , :
40	instantiation	43, 44, 45	⊢
	: , : , :
41	assumption		⊢
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
43	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat4