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	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
2	reference	53	⊢
3	instantiation	26	⊢
	: , :
4	instantiation	26	⊢
	: , :
5	instantiation	22, 7, 8	,  ⊢
	: , :
6	instantiation	9, 10, 11, 23, 24, 12*	, , ,  ⊢
	: , : , : , : , :
7	instantiation	54, 40, 13	⊢
	: , : , :
8	instantiation	54, 40, 37	⊢
	: , : , :
9	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
10	instantiation	14, 16, 17, 18	⊢
	: , : , :
11	instantiation	15, 16, 17, 18, 19, 20, 21	,  ⊢
	: , : , : , :
12	instantiation	22, 23, 24	,  ⊢
	: , :
13	assumption		⊢
14	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
15	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
16	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
17	instantiation	26	⊢
	: , :
18	instantiation	25, 34	⊢
	:
19	instantiation	26	⊢
	: , :
20	instantiation	28, 29, 27	⊢
	: , : , :
21	instantiation	28, 29, 30	⊢
	: , : , :
22	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
23	instantiation	54, 40, 31	⊢
	: , : , :
24	instantiation	54, 40, 32	⊢
	: , : , :
25	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
26	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
27	assumption		⊢
28	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
29	instantiation	33, 34, 35	⊢
	: , : , :
30	assumption		⊢
31	assumption		⊢
32	instantiation	36, 37, 38	⊢
	: , :
33	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
34	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
35	instantiation	39, 40	⊢
	: , :
36	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
37	instantiation	54, 42, 41	⊢
	: , : , :
38	instantiation	54, 42, 43	⊢
	: , : , :
39	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
41	instantiation	54, 45, 44	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
43	instantiation	54, 45, 46	⊢
	: , : , :
44	instantiation	54, 47, 48	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
46	instantiation	54, 55, 49	⊢
	: , : , :
47	instantiation	50, 51, 52	⊢
	: , :
48	assumption		⊢
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
50	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
51	instantiation	54, 55, 53	⊢
	: , : , :
52	instantiation	54, 55, 56	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
54	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
55	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
56	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
*equality replacement requirements