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	generalization	1	, ,  ⊢
1	instantiation	13, 2, 3	, , ,  ⊢
	: , : , :
2	instantiation	4, 5, 6, 7	, , ,  ⊢
	: , : , : , :
3	instantiation	8, 9, 10, 11	, , ,  ⊢
	: , : , : , :
4	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
5	instantiation	12, 15, 16, 31	⊢
	: , : , :
6	instantiation	13, 27, 35	,  ⊢
	: , : , :
7	instantiation	14, 15, 16, 31, 17, 32, 33	,  ⊢
	: , : , : , :
8	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
9	instantiation	18, 19, 20	, , ,  ⊢
	: , : , :
10	instantiation	21	⊢
	:
11	instantiation	22, 23	,  ⊢
	: , :
12	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
13	theorem		⊢
	proveit.logic.equality.sub_left_side_into
14	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
15	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
16	instantiation	24	⊢
	: , :
17	instantiation	24	⊢
	: , :
18	axiom		⊢
	proveit.logic.equality.equals_transitivity
19	instantiation	34, 25	,  ⊢
	: , : , :
20	instantiation	26, 27, 28, 29, 30, 31, 32, 33	, , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
21	axiom		⊢
	proveit.logic.equality.equals_reflexivity
22	theorem		⊢
	proveit.logic.equality.equals_reversal
23	instantiation	34, 35	,  ⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
25	instantiation	34, 35	,  ⊢
	: , : , :
26	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
27	instantiation	36, 42, 44	,  ⊢
	: , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
29	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
30	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
31	instantiation	37, 38	⊢
	:
32	assumption		⊢
33	assumption		⊢
34	axiom		⊢
	proveit.logic.equality.substitution
35	instantiation	39, 40, 41	,  ⊢
	: , :
36	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
37	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
38	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
39	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
40	instantiation	55, 43, 42	⊢
	: , : , :
41	instantiation	55, 43, 44	⊢
	: , : , :
42	assumption		⊢
43	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
44	instantiation	55, 45, 46	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
46	instantiation	55, 47, 48	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
48	instantiation	55, 49, 50	⊢
	: , : , :
49	instantiation	51, 52, 53	⊢
	: , :
50	assumption		⊢
51	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
52	instantiation	55, 56, 54	⊢
	: , : , :
53	instantiation	55, 56, 57	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
55	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
56	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat4