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