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