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	axiom		⊢
	proveit.logic.equality.substitution
2	modus ponens	5, 6	, , , ,  ⊢
3	instantiation	7, 55	⊢
	: , :
4	instantiation	7, 55	⊢
	: , :
5	instantiation	8, 9	⊢
	: , : , : , : , : , : , :
6	generalization	10	, , , ,  ⊢
7	theorem		⊢
	proveit.core_expr_types.conditionals.satisfied_condition_reduction
8	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
9	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
10	instantiation	11, 12, 13, 14, 15	, , , , ,  ⊢
	: , : , : , : , :
11	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
12	instantiation	16, 36, 18, 19	⊢
	: , : , :
13	instantiation	17, 36, 18, 19, 20, 21, 22, 23	, , ,  ⊢
	: , : , : , :
14	instantiation	57, 42, 24	⊢
	: , : , :
15	instantiation	57, 42, 25	⊢
	: , : , :
16	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
17	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
18	instantiation	27	⊢
	: , : , :
19	instantiation	26, 36	⊢
	:
20	instantiation	27	⊢
	: , : , :
21	instantiation	30, 31, 28	⊢
	: , : , :
22	instantiation	30, 31, 29	,  ⊢
	: , : , :
23	instantiation	30, 31, 32	⊢
	: , : , :
24	assumption		⊢
25	assumption		⊢
26	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
28	assumption		⊢
29	instantiation	33, 34	,  ⊢
	:
30	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
31	instantiation	35, 36, 37	⊢
	: , : , :
32	assumption		⊢
33	assumption		⊢
34	instantiation	38, 39, 40	⊢
	:
35	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
37	instantiation	41, 42	⊢
	: , :
38	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
39	instantiation	57, 43, 55	⊢
	: , : , :
40	instantiation	44, 45	⊢
	: , :
41	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
42	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
43	instantiation	46, 53, 54	⊢
	: , :
44	theorem		⊢
	proveit.numbers.ordering.relax_less
45	instantiation	47, 48, 49	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
47	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
48	instantiation	50, 51	⊢
	:
49	instantiation	52, 53, 54, 55	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
51	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
52	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
53	instantiation	57, 58, 56	⊢
	: , : , :
54	instantiation	57, 58, 59	⊢
	: , : , :
55	assumption		⊢
56	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
57	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
*equality replacement requirements