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, 5, 6*	, , ,  ⊢
	: , : , : , : , :
1	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
2	instantiation	7, 9, 10, 11	⊢
	: , : , :
3	instantiation	8, 9, 10, 11, 12, 13, 14	,  ⊢
	: , : , : , :
4	reference	16	⊢
5	reference	17	⊢
6	instantiation	15, 16, 17	,  ⊢
	: , :
7	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
8	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
9	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
10	instantiation	19	⊢
	: , :
11	instantiation	18, 27	⊢
	:
12	instantiation	19	⊢
	: , :
13	instantiation	21, 22, 20	⊢
	: , : , :
14	instantiation	21, 22, 23	⊢
	: , : , :
15	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
16	instantiation	41, 32, 24	⊢
	: , : , :
17	instantiation	41, 32, 25	⊢
	: , : , :
18	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
19	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
20	assumption		⊢
21	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
22	instantiation	26, 27, 28	⊢
	: , : , :
23	assumption		⊢
24	assumption		⊢
25	instantiation	41, 29, 30	⊢
	: , : , :
26	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
27	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
28	instantiation	31, 32	⊢
	: , :
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
30	instantiation	41, 33, 34	⊢
	: , : , :
31	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
32	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
33	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
34	instantiation	41, 35, 36	⊢
	: , : , :
35	instantiation	37, 38, 39	⊢
	: , :
36	assumption		⊢
37	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
38	instantiation	41, 42, 40	⊢
	: , : , :
39	instantiation	41, 42, 43	⊢
	: , : , :
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
*equality replacement requirements