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, 7*, 8*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
2	instantiation	9, 17	⊢
	:
3	instantiation	10, 17, 11	⊢
	: , :
4	reference	18	⊢
5	instantiation	13, 24, 12	⊢
	: , :
6	instantiation	13, 24, 14	⊢
	: , :
7	instantiation	16, 17, 62, 18, 19, 15*	⊢
	: , : , :
8	instantiation	16, 17, 21, 18, 19, 20*	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.exponentiation.sqrt_complex_closure
10	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
11	instantiation	83, 63, 21	⊢
	: , : , :
12	instantiation	22, 23, 24	⊢
	: , :
13	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
14	instantiation	83, 25, 45	⊢
	: , : , :
15	instantiation	26, 55, 50, 27*	⊢
	: , :
16	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
17	instantiation	83, 63, 28	⊢
	: , : , :
18	instantiation	83, 66, 29	⊢
	: , : , :
19	instantiation	30, 85	⊢
	:
20	instantiation	31, 32, 33	⊢
	: , : , :
21	instantiation	83, 66, 34	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.division.div_rational_nonzero_closure
23	instantiation	83, 36, 35	⊢
	: , : , :
24	instantiation	83, 36, 37	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational_nonzero
26	theorem		⊢
	proveit.numbers.negation.pos_times_neg
27	instantiation	38, 55	⊢
	:
28	instantiation	83, 66, 39	⊢
	: , : , :
29	instantiation	83, 71, 40	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
31	axiom		⊢
	proveit.logic.equality.equals_transitivity
32	instantiation	41, 52, 59, 78, 54, 53, 55, 56, 42	⊢
	: , : , : , : , : , :
33	instantiation	43, 59, 52, 53, 54, 55, 56, 50, 44*	⊢
	: , : , : , : , :
34	instantiation	83, 73, 45	⊢
	: , : , :
35	instantiation	83, 46, 82	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
37	instantiation	83, 46, 85	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
39	instantiation	83, 71, 47	⊢
	: , : , :
40	instantiation	48, 72	⊢
	:
41	theorem		⊢
	proveit.numbers.multiplication.disassociation
42	instantiation	49, 50	⊢
	:
43	theorem		⊢
	proveit.numbers.multiplication.mult_neg_any
44	instantiation	51, 59, 52, 53, 54, 55, 56	⊢
	: , : , : , :
45	instantiation	57, 74, 58	⊢
	: , :
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
47	instantiation	83, 77, 59	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.negation.int_closure
49	theorem		⊢
	proveit.numbers.negation.complex_closure
50	instantiation	83, 63, 60	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
52	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
53	instantiation	61	⊢
	: , :
54	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
55	instantiation	83, 63, 62	⊢
	: , : , :
56	instantiation	83, 63, 64	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.multiplication.mult_rational_pos_closure_bin
58	instantiation	83, 84, 70	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
60	instantiation	83, 66, 65	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
62	instantiation	83, 66, 67	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
64	instantiation	68, 69, 70	⊢
	: , : , :
65	instantiation	83, 71, 72	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
67	instantiation	83, 73, 74	⊢
	: , : , :
68	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
69	instantiation	75, 76	⊢
	: , :
70	assumption		⊢
71	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
72	instantiation	83, 77, 78	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
74	instantiation	79, 80, 81	⊢
	: , :
75	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
76	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
77	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
78	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
79	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
80	instantiation	83, 84, 82	⊢
	: , : , :
81	instantiation	83, 84, 85	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
83	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
84	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
85	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
*equality replacement requirements