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