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, 6*	,  ⊢
	: , :
1	theorem		⊢
	proveit.numbers.absolute_value.abs_prod
2	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
3	instantiation	28	⊢
	: , :
4	reference	35	⊢
5	instantiation	7, 8, 9	⊢
	: , :
6	instantiation	10, 11, 12	,  ⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
8	instantiation	45, 39, 13	⊢
	: , : , :
9	instantiation	14, 15, 16	⊢
	: , :
10	axiom		⊢
	proveit.logic.equality.equals_transitivity
11	instantiation	17, 18, 19, 20, 21, 22	,  ⊢
	: , : , : , :
12	instantiation	23, 35, 24, 25*	⊢
	: , :
13	instantiation	45, 26, 27	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
15	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
16	instantiation	45, 39, 32	⊢
	: , : , :
17	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
18	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
19	instantiation	28	⊢
	: , :
20	instantiation	28	⊢
	: , :
21	instantiation	29, 30	⊢
	:
22	instantiation	31, 32	⊢
	:
23	theorem		⊢
	proveit.numbers.negation.neg_times_pos
24	instantiation	45, 39, 33	⊢
	: , : , :
25	instantiation	34, 35	⊢
	:
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
28	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
29	theorem		⊢
	proveit.numbers.absolute_value.abs_neg_elim
30	instantiation	36, 44	⊢
	:
31	theorem		⊢
	proveit.numbers.absolute_value.complex_unit_length
32	assumption		⊢
33	instantiation	45, 37, 38	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
35	instantiation	45, 39, 40	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonpos_if_in_real_nonpos
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
38	instantiation	45, 41, 42	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
40	instantiation	45, 43, 44	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
42	instantiation	45, 46, 47	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonpos_within_real
44	assumption		⊢
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.nat1
*equality replacement requirements