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	modus ponens	1, 2	, ,  ⊢
1	instantiation	3, 4	⊢
	: , : , : , : , : , : , :
2	generalization	5	, ,  ⊢
3	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
4	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
5	instantiation	6, 7, 8, 19, 20, 9*	, , ,  ⊢
	: , : , : , : , :
6	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
7	instantiation	10, 12, 13, 14	⊢
	: , : , :
8	instantiation	11, 12, 13, 14, 15, 16, 17	,  ⊢
	: , : , : , :
9	instantiation	18, 19, 20	,  ⊢
	: , :
10	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
11	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
12	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
13	instantiation	22	⊢
	: , :
14	instantiation	21, 30	⊢
	:
15	instantiation	22	⊢
	: , :
16	instantiation	24, 25, 23	⊢
	: , : , :
17	instantiation	24, 25, 26	⊢
	: , : , :
18	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
19	instantiation	44, 35, 27	⊢
	: , : , :
20	instantiation	44, 35, 28	⊢
	: , : , :
21	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
22	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
23	assumption		⊢
24	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
25	instantiation	29, 30, 31	⊢
	: , : , :
26	assumption		⊢
27	assumption		⊢
28	instantiation	44, 32, 33	⊢
	: , : , :
29	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
30	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
31	instantiation	34, 35	⊢
	: , :
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
33	instantiation	44, 36, 37	⊢
	: , : , :
34	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
36	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
37	instantiation	44, 38, 39	⊢
	: , : , :
38	instantiation	40, 41, 42	⊢
	: , :
39	assumption		⊢
40	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
41	instantiation	44, 45, 43	⊢
	: , : , :
42	instantiation	44, 45, 46	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
44	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
45	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
*equality replacement requirements