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	10	⊢
2	instantiation	28, 4	,  ⊢
	: , : , :
3	instantiation	5, 39, 6, 7, 8, 37, 9, 22	, ,  ⊢
	: , : , : , : , : , : , : , : , : , :
4	instantiation	10, 11, 12	,  ⊢
	: , : , :
5	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
6	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
7	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
8	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
9	assumption		⊢
10	axiom		⊢
	proveit.logic.equality.equals_transitivity
11	instantiation	28, 13, 14*, 15*	⊢
	: , : , :
12	instantiation	16, 17	,  ⊢
	: , :
13	modus ponens	18, 19	⊢
14	instantiation	20, 49	⊢
	: , :
15	instantiation	20, 49	⊢
	: , :
16	theorem		⊢
	proveit.logic.equality.equals_reversal
17	modus ponens	21, 22	,  ⊢
18	instantiation	23, 31	⊢
	: , : , : , : , : , : , :
19	generalization	24	⊢
20	theorem		⊢
	proveit.core_expr_types.conditionals.satisfied_condition_reduction
21	instantiation	25, 31, 37, 39	⊢
	: , : , : , : , : , : , : , :
22	modus ponens	26, 27	⊢
23	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
24	instantiation	28, 29	,  ⊢
	: , : , :
25	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum_with_scalar_mult
26	instantiation	30, 31, 37	⊢
	: , : , : , : , : , :
27	generalization	32	⊢
28	axiom		⊢
	proveit.logic.equality.substitution
29	instantiation	33, 34, 35	,  ⊢
	: , :
30	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
31	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
32	instantiation	36, 37, 41, 38	,  ⊢
	: , : , : , :
33	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
34	instantiation	54, 40, 39	⊢
	: , : , :
35	instantiation	54, 40, 41	⊢
	: , : , :
36	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
37	instantiation	42, 43	⊢
	:
38	assumption		⊢
39	assumption		⊢
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
41	instantiation	54, 44, 45	⊢
	: , : , :
42	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
43	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
45	instantiation	54, 46, 47	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
47	instantiation	54, 48, 49	⊢
	: , : , :
48	instantiation	50, 51, 52	⊢
	: , :
49	assumption		⊢
50	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
51	instantiation	54, 55, 53	⊢
	: , : , :
52	instantiation	54, 55, 56	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
54	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
55	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
56	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
*equality replacement requirements