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	29, 4	,  ⊢
	: , : , :
3	instantiation	5, 6	, ,  ⊢
	: , :
4	modus ponens	7, 8	,  ⊢
5	theorem		⊢
	proveit.logic.equality.equals_reversal
6	modus ponens	9, 10	, ,  ⊢
7	instantiation	11, 21	⊢
	: , : , : , : , : , :
8	generalization	12	,  ⊢
9	instantiation	13, 21, 22, 14	,  ⊢
	: , : , : , : , : , : , :
10	modus ponens	15, 16	⊢
11	axiom		⊢
	proveit.core_expr_types.lambda_maps.lambda_substitution
12	instantiation	17, 18	,  ⊢
	: , : , :
13	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum
14	instantiation	19, 40, 42	,  ⊢
	: , :
15	instantiation	20, 21, 22	⊢
	: , : , : , : , : , :
16	generalization	23	⊢
17	axiom		⊢
	proveit.core_expr_types.conditionals.conditional_substitution
18	deduction	24	,  ⊢
19	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
20	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
21	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
22	instantiation	25, 26	⊢
	:
23	instantiation	27, 28	,  ⊢
	:
24	instantiation	29, 30	,  ⊢
	: , : , :
25	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
26	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
27	assumption		⊢
28	instantiation	31, 32, 33	⊢
	:
29	axiom		⊢
	proveit.logic.equality.substitution
30	instantiation	34, 35, 36	,  ⊢
	: , :
31	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
32	instantiation	54, 37, 52	⊢
	: , : , :
33	instantiation	38, 39	⊢
	: , :
34	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
35	instantiation	54, 41, 40	⊢
	: , : , :
36	instantiation	54, 41, 42	⊢
	: , : , :
37	instantiation	43, 50, 51	⊢
	: , :
38	theorem		⊢
	proveit.numbers.ordering.relax_less
39	instantiation	44, 45, 46	⊢
	: , : , :
40	assumption		⊢
41	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
42	assumption		⊢
43	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
44	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
45	instantiation	47, 48	⊢
	:
46	instantiation	49, 50, 51, 52	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
48	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
49	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
50	instantiation	54, 55, 53	⊢
	: , : , :
51	instantiation	54, 55, 56	⊢
	: , : , :
52	assumption		⊢
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