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	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
2	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
3	instantiation	7	⊢
	: , :
4	instantiation	7	⊢
	: , :
5	instantiation	8, 9	⊢
	:
6	instantiation	10, 11, 12*	⊢
	:
7	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
8	theorem		⊢
	proveit.numbers.absolute_value.abs_non_neg_elim
9	instantiation	13, 14	⊢
	:
10	theorem		⊢
	proveit.numbers.absolute_value.complex_unit_length
11	instantiation	15, 31	⊢
	:
12	instantiation	23, 16	⊢
	: , :
13	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonneg_if_in_real_nonneg
14	assumption		⊢
15	theorem		⊢
	proveit.numbers.negation.real_closure
16	instantiation	21, 17	⊢
	: , : , :
17	instantiation	18, 19, 20	⊢
	: , : , :
18	axiom		⊢
	proveit.logic.equality.equals_transitivity
19	instantiation	21, 22	⊢
	: , : , :
20	instantiation	23, 24	⊢
	: , :
21	axiom		⊢
	proveit.logic.equality.substitution
22	instantiation	25, 28, 27	⊢
	: , :
23	theorem		⊢
	proveit.logic.equality.equals_reversal
24	instantiation	26, 27, 28	⊢
	: , :
25	theorem		⊢
	proveit.numbers.multiplication.commutation
26	theorem		⊢
	proveit.numbers.negation.pos_times_neg
27	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
28	instantiation	29, 30, 31	⊢
	: , : , :
29	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
30	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
31	assumption		⊢
*equality replacement requirements