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, 4	, , , , ,  ⊢
	: , : , : , :
1	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
2	instantiation	5, 21, 10, 11	⊢
	: , : , :
3	instantiation	6, 7, 8	,  ⊢
	: , : , :
4	instantiation	9, 21, 10, 11, 12, 13, 14, 15	, , ,  ⊢
	: , : , : , :
5	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
6	theorem		⊢
	proveit.logic.equality.sub_left_side_into
7	instantiation	16, 25, 27	,  ⊢
	: , :
8	instantiation	17, 18, 19	,  ⊢
	: , :
9	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
10	instantiation	22	⊢
	: , : , :
11	instantiation	20, 21	⊢
	:
12	instantiation	22	⊢
	: , : , :
13	assumption		⊢
14	instantiation	23, 24	,  ⊢
	:
15	assumption		⊢
16	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
17	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
18	instantiation	45, 26, 25	⊢
	: , : , :
19	instantiation	45, 26, 27	⊢
	: , : , :
20	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
21	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
22	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
23	assumption		⊢
24	instantiation	28, 29, 30	⊢
	:
25	assumption		⊢
26	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
27	assumption		⊢
28	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
29	instantiation	45, 31, 43	⊢
	: , : , :
30	instantiation	32, 33	⊢
	: , :
31	instantiation	34, 41, 42	⊢
	: , :
32	theorem		⊢
	proveit.numbers.ordering.relax_less
33	instantiation	35, 36, 37	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
35	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
36	instantiation	38, 39	⊢
	:
37	instantiation	40, 41, 42, 43	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
40	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
41	instantiation	45, 46, 44	⊢
	: , : , :
42	instantiation	45, 46, 47	⊢
	: , : , :
43	assumption		⊢
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
45	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat4