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