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	theorem		⊢
	proveit.logic.equality.sub_left_side_into
2	instantiation	4, 5, 8, 6	, ,  ⊢
	: , : , : , :
3	instantiation	7, 8, 35, 9, 10, 15, 17, 18	, ,  ⊢
	: , : , : , : , : , : , : , : , : , :
4	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
5	instantiation	11, 13, 14, 15	⊢
	: , : , :
6	instantiation	12, 13, 14, 15, 16, 17, 18	,  ⊢
	: , : , : , :
7	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
8	instantiation	19, 25, 20	⊢
	: , :
9	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
10	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
11	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
12	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
13	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
14	instantiation	23	⊢
	: , :
15	instantiation	21, 22	⊢
	:
16	instantiation	23	⊢
	: , :
17	assumption		⊢
18	assumption		⊢
19	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
20	instantiation	24, 25, 26	⊢
	: , :
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	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
25	instantiation	40, 28, 27	⊢
	: , : , :
26	instantiation	40, 28, 29	⊢
	: , : , :
27	instantiation	40, 31, 30	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
29	instantiation	40, 31, 32	⊢
	: , : , :
30	instantiation	40, 33, 34	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
32	instantiation	40, 41, 35	⊢
	: , : , :
33	instantiation	36, 37, 38	⊢
	: , :
34	assumption		⊢
35	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
36	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
37	instantiation	40, 41, 39	⊢
	: , : , :
38	instantiation	40, 41, 42	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
40	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
41	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat4