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