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	reference	55	⊢
2	instantiation	79, 5, 6*, 7*	, ,  ⊢
	: , : , :
3	instantiation	59, 8	, ,  ⊢
	: , :
4	instantiation	55, 9, 10	, ,  ⊢
	: , : , :
5	modus ponens	11, 12	, ,  ⊢
6	instantiation	43, 98	⊢
	: , :
7	instantiation	43, 98	⊢
	: , :
8	modus ponens	13, 14	, ,  ⊢
9	instantiation	79, 15	,  ⊢
	: , : , :
10	instantiation	69, 90, 71, 72, 73, 83, 74, 45	, ,  ⊢
	: , : , : , : , : , : , : , : , : , :
11	instantiation	61, 76	⊢
	: , : , : , : , : , : , :
12	generalization	16	, ,  ⊢
13	instantiation	17, 71, 76, 72, 34, 73	⊢
	: , : , : , : , : , : , : , : , : , : , :
14	generalization	18	, ,  ⊢
15	instantiation	55, 19, 20	,  ⊢
	: , : , :
16	instantiation	21, 22, 23, 86, 87	, , ,  ⊢
	: , : , : , : , :
17	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation_with_scalar_mult
18	instantiation	50, 24, 25	, , ,  ⊢
	: , : , :
19	instantiation	79, 26, 27*, 28*	⊢
	: , : , :
20	instantiation	59, 29	,  ⊢
	: , :
21	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
22	instantiation	49, 52, 30, 31	⊢
	: , : , :
23	instantiation	51, 52, 30, 31, 54, 32, 33	,  ⊢
	: , : , : , :
24	instantiation	82, 34, 35, 36	, , ,  ⊢
	: , : , : , :
25	instantiation	37, 38, 39, 40	, , ,  ⊢
	: , : , : , :
26	modus ponens	41, 42	⊢
27	instantiation	43, 98	⊢
	: , :
28	instantiation	43, 98	⊢
	: , :
29	modus ponens	44, 45	,  ⊢
30	instantiation	67	⊢
	: , :
31	instantiation	46, 89	⊢
	:
32	instantiation	47, 48, 74	⊢
	: , : , :
33	instantiation	47, 48, 84	⊢
	: , : , :
34	instantiation	49, 52, 53, 83	⊢
	: , : , :
35	instantiation	50, 70, 80	,  ⊢
	: , : , :
36	instantiation	51, 52, 53, 83, 54, 74, 84	,  ⊢
	: , : , : , :
37	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
38	instantiation	55, 56, 57	, , ,  ⊢
	: , : , :
39	instantiation	58	⊢
	:
40	instantiation	59, 60	,  ⊢
	: , :
41	instantiation	61, 76	⊢
	: , : , : , : , : , : , :
42	generalization	68	⊢
43	theorem		⊢
	proveit.core_expr_types.conditionals.satisfied_condition_reduction
44	instantiation	62, 76, 83, 90	⊢
	: , : , : , : , : , : , : , :
45	modus ponens	63, 64	⊢
46	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
47	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
48	instantiation	65, 89, 66	⊢
	: , : , :
49	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
50	theorem		⊢
	proveit.logic.equality.sub_left_side_into
51	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
52	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
53	instantiation	67	⊢
	: , :
54	instantiation	67	⊢
	: , :
55	axiom		⊢
	proveit.logic.equality.equals_transitivity
56	instantiation	79, 68	,  ⊢
	: , : , :
57	instantiation	69, 70, 71, 72, 73, 83, 74, 84	, , ,  ⊢
	: , : , : , : , : , : , : , : , : , :
58	axiom		⊢
	proveit.logic.equality.equals_reflexivity
59	theorem		⊢
	proveit.logic.equality.equals_reversal
60	instantiation	79, 80	,  ⊢
	: , : , :
61	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
62	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum_with_scalar_mult
63	instantiation	75, 76, 83	⊢
	: , : , : , : , : , :
64	generalization	77	⊢
65	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
66	instantiation	78, 91	⊢
	: , :
67	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
68	instantiation	79, 80	,  ⊢
	: , : , :
69	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
70	instantiation	81, 90, 92	,  ⊢
	: , :
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
72	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
73	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
74	assumption		⊢
75	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
76	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
77	instantiation	82, 83, 92, 84	,  ⊢
	: , : , : , :
78	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
79	axiom		⊢
	proveit.logic.equality.substitution
80	instantiation	85, 86, 87	,  ⊢
	: , :
81	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
82	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
83	instantiation	88, 89	⊢
	:
84	assumption		⊢
85	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
86	instantiation	103, 91, 90	⊢
	: , : , :
87	instantiation	103, 91, 92	⊢
	: , : , :
88	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
89	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
90	assumption		⊢
91	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
92	instantiation	103, 93, 94	⊢
	: , : , :
93	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
94	instantiation	103, 95, 96	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
96	instantiation	103, 97, 98	⊢
	: , : , :
97	instantiation	99, 100, 101	⊢
	: , :
98	assumption		⊢
99	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
100	instantiation	103, 104, 102	⊢
	: , : , :
101	instantiation	103, 104, 105	⊢
	: , : , :
102	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
103	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
104	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
105	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
*equality replacement requirements