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, 74	⊢
	: , :
4	instantiation	7, 74	⊢
	: , :
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	35, 11, 12	, , , ,  ⊢
	: , : , :
11	instantiation	13, 79, 14, 15, 16, 17	, , , ,  ⊢
	: , : , : , :
12	instantiation	19, 20, 21, 23, 44, 18*	, , , ,  ⊢
	: , : , : , : , :
13	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
14	instantiation	58	⊢
	: , :
15	instantiation	58	⊢
	: , :
16	instantiation	33, 50, 51	,  ⊢
	: , :
17	instantiation	19, 20, 21, 56, 57, 22*	, , ,  ⊢
	: , : , : , : , :
18	instantiation	33, 23, 44, 24*	, ,  ⊢
	: , :
19	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
20	instantiation	25, 27, 28, 29	⊢
	: , : , :
21	instantiation	26, 27, 28, 29, 30, 31, 32	,  ⊢
	: , : , : , :
22	instantiation	33, 56, 57	,  ⊢
	: , :
23	instantiation	80, 62, 34	,  ⊢
	: , : , :
24	instantiation	35, 36, 37	, ,  ⊢
	: , : , :
25	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
26	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
27	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
28	instantiation	58	⊢
	: , :
29	instantiation	38, 53	⊢
	:
30	instantiation	58	⊢
	: , :
31	instantiation	40, 41, 39	⊢
	: , : , :
32	instantiation	40, 41, 42	⊢
	: , : , :
33	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
34	instantiation	43, 59, 65	,  ⊢
	: , :
35	axiom		⊢
	proveit.logic.equality.equals_transitivity
36	instantiation	45, 46, 79, 75, 49, 47, 50, 51, 44	, ,  ⊢
	: , : , : , : , : , :
37	instantiation	45, 79, 46, 47, 48, 49, 50, 51, 56, 57	, ,  ⊢
	: , : , : , : , : , :
38	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
39	assumption		⊢
40	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
41	instantiation	52, 53, 54	⊢
	: , : , :
42	assumption		⊢
43	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
44	instantiation	55, 56, 57	,  ⊢
	: , :
45	theorem		⊢
	proveit.numbers.multiplication.disassociation
46	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
47	instantiation	58	⊢
	: , :
48	instantiation	58	⊢
	: , :
49	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
50	instantiation	80, 62, 59	⊢
	: , : , :
51	instantiation	80, 62, 65	⊢
	: , : , :
52	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
53	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
54	instantiation	60, 62	⊢
	: , :
55	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
56	instantiation	80, 62, 61	⊢
	: , : , :
57	instantiation	80, 62, 63	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
59	assumption		⊢
60	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
61	assumption		⊢
62	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
63	instantiation	64, 65, 66	⊢
	: , :
64	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
65	instantiation	80, 68, 67	⊢
	: , : , :
66	instantiation	80, 68, 69	⊢
	: , : , :
67	instantiation	80, 71, 70	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
69	instantiation	80, 71, 72	⊢
	: , : , :
70	instantiation	80, 73, 74	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
72	instantiation	80, 81, 75	⊢
	: , : , :
73	instantiation	76, 77, 78	⊢
	: , :
74	assumption		⊢
75	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
76	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
77	instantiation	80, 81, 79	⊢
	: , : , :
78	instantiation	80, 81, 82	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
80	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
81	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
82	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
*equality replacement requirements