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, 5*	, , , ,  ⊢
	: , : , : , :
1	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
2	instantiation	10, 6, 7*, 8*	, , , ,  ⊢
	: , : , :
3	instantiation	17, 9	, , , ,  ⊢
	: , :
4	instantiation	10, 11	, ,  ⊢
	: , : , :
5	reference	31	,  ⊢
6	modus ponens	12, 13	, , , ,  ⊢
7	instantiation	14, 84	⊢
	: , :
8	instantiation	14, 84	⊢
	: , :
9	modus ponens	15, 16	, , , ,  ⊢
10	axiom		⊢
	proveit.logic.equality.substitution
11	instantiation	17, 18	, ,  ⊢
	: , :
12	instantiation	19, 35	⊢
	: , : , : , : , : , : , :
13	generalization	20	, , , ,  ⊢
14	theorem		⊢
	proveit.core_expr_types.conditionals.satisfied_condition_reduction
15	instantiation	21, 35, 36, 22	,  ⊢
	: , : , : , : , : , : , :
16	modus ponens	23, 25	, ,  ⊢
17	theorem		⊢
	proveit.logic.equality.equals_reversal
18	modus ponens	24, 25	, ,  ⊢
19	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
20	instantiation	26, 27, 28, 45, 46	, , , , ,  ⊢
	: , : , : , : , :
21	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum
22	instantiation	29, 30, 31	,  ⊢
	: , : , :
23	instantiation	32, 35, 36	⊢
	: , : , : , : , : , :
24	instantiation	33, 34, 35, 36	⊢
	: , : , : , : , : , : , : , : , : , :
25	generalization	37	, ,  ⊢
26	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
27	instantiation	47, 65, 38, 39	⊢
	: , : , :
28	instantiation	48, 65, 38, 39, 51, 40, 41, 42	, , ,  ⊢
	: , : , : , :
29	theorem		⊢
	proveit.logic.equality.sub_left_side_into
30	instantiation	43, 58, 59	,  ⊢
	: , :
31	instantiation	44, 45, 46	,  ⊢
	: , :
32	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
33	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation
34	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
35	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
36	instantiation	47, 65, 49, 50	⊢
	: , : , :
37	instantiation	48, 65, 49, 50, 51, 53, 54, 57	, , ,  ⊢
	: , : , : , :
38	instantiation	61	⊢
	: , : , :
39	instantiation	52, 65	⊢
	:
40	instantiation	55, 56, 53	⊢
	: , : , :
41	instantiation	55, 56, 54	,  ⊢
	: , : , :
42	instantiation	55, 56, 57	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
44	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
45	instantiation	86, 71, 58	⊢
	: , : , :
46	instantiation	86, 71, 59	⊢
	: , : , :
47	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
48	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
49	instantiation	61	⊢
	: , : , :
50	instantiation	60, 65	⊢
	:
51	instantiation	61	⊢
	: , : , :
52	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
53	assumption		⊢
54	instantiation	62, 63	,  ⊢
	:
55	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
56	instantiation	64, 65, 66	⊢
	: , : , :
57	assumption		⊢
58	assumption		⊢
59	assumption		⊢
60	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
61	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
62	assumption		⊢
63	instantiation	67, 68, 69	⊢
	:
64	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
65	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
66	instantiation	70, 71	⊢
	: , :
67	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
68	instantiation	86, 72, 84	⊢
	: , : , :
69	instantiation	73, 74	⊢
	: , :
70	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
71	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
72	instantiation	75, 82, 83	⊢
	: , :
73	theorem		⊢
	proveit.numbers.ordering.relax_less
74	instantiation	76, 77, 78	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
76	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
77	instantiation	79, 80	⊢
	:
78	instantiation	81, 82, 83, 84	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
80	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
81	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
82	instantiation	86, 87, 85	⊢
	: , : , :
83	instantiation	86, 87, 88	⊢
	: , : , :
84	assumption		⊢
85	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
86	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
87	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
88	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
*equality replacement requirements