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*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
2	reference	12	⊢
3	reference	48	⊢
4	instantiation	102, 81, 8	⊢
	: , : , :
5	instantiation	88, 42	⊢
	:
6	instantiation	52, 38, 9	⊢
	: , :
7	instantiation	13, 10, 11	⊢
	: , : , :
8	instantiation	102, 94, 32	⊢
	: , : , :
9	instantiation	102, 66, 12	⊢
	: , : , :
10	instantiation	13, 14, 15	⊢
	: , : , :
11	instantiation	16, 17, 18	⊢
	: , :
12	instantiation	102, 81, 19	⊢
	: , : , :
13	axiom		⊢
	proveit.logic.equality.equals_transitivity
14	instantiation	46, 26	⊢
	: , : , :
15	instantiation	46, 20	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
17	instantiation	21, 22, 23	⊢
	: , :
18	instantiation	24	⊢
	:
19	instantiation	102, 94, 25	⊢
	: , : , :
20	instantiation	46, 26	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
22	instantiation	27, 38, 28, 29	⊢
	: , :
23	instantiation	102, 66, 30	⊢
	: , : , :
24	axiom		⊢
	proveit.logic.equality.equals_reflexivity
25	instantiation	31, 32	⊢
	:
26	instantiation	33, 34, 35, 36	⊢
	: , : , : , :
27	theorem		⊢
	proveit.numbers.division.div_complex_closure
28	instantiation	37, 56, 38	⊢
	: , :
29	instantiation	39, 57, 40	⊢
	: , : , :
30	instantiation	77, 78, 41	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.negation.int_closure
32	instantiation	102, 86, 42	⊢
	: , : , :
33	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
34	instantiation	46, 43	⊢
	: , : , :
35	instantiation	44, 45	⊢
	: , :
36	instantiation	46, 47	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
38	instantiation	102, 66, 48	⊢
	: , : , :
39	theorem		⊢
	proveit.logic.equality.sub_left_side_into
40	instantiation	49, 56	⊢
	:
41	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
42	instantiation	50, 101, 51	⊢
	: , :
43	instantiation	52, 53, 54	⊢
	: , :
44	theorem		⊢
	proveit.logic.equality.equals_reversal
45	instantiation	55, 56, 65, 64, 57	⊢
	: , : , :
46	axiom		⊢
	proveit.logic.equality.substitution
47	instantiation	58, 59, 106	⊢
	: , :
48	instantiation	102, 81, 60	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
50	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
51	instantiation	61, 62, 63	⊢
	:
52	theorem		⊢
	proveit.numbers.addition.commutation
53	instantiation	102, 66, 64	⊢
	: , : , :
54	instantiation	102, 66, 65	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
56	instantiation	102, 66, 67	⊢
	: , : , :
57	instantiation	68, 104	⊢
	:
58	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
59	instantiation	102, 69, 70	⊢
	: , : , :
60	instantiation	102, 94, 71	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
62	instantiation	72, 73, 74	⊢
	: , :
63	instantiation	75, 76	⊢
	: , :
64	instantiation	77, 78, 89	⊢
	: , : , :
65	instantiation	102, 79, 80	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
67	instantiation	102, 81, 82	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
69	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
70	instantiation	102, 83, 84	⊢
	: , : , :
71	instantiation	102, 100, 85	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
73	instantiation	102, 86, 89	⊢
	: , : , :
74	instantiation	102, 87, 99	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
76	instantiation	88, 89	⊢
	:
77	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
78	instantiation	90, 91	⊢
	: , :
79	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
80	instantiation	102, 92, 93	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
82	instantiation	102, 94, 95	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
84	instantiation	102, 96, 97	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
86	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
87	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
88	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
89	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
90	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
91	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
92	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
93	instantiation	102, 98, 99	⊢
	: , : , :
94	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
95	instantiation	102, 100, 101	⊢
	: , : , :
96	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
97	instantiation	102, 103, 104	⊢
	: , : , :
98	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
99	instantiation	105, 106	⊢
	:
100	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
101	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
102	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
103	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
104	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
105	theorem		⊢
	proveit.numbers.negation.int_neg_closure
106	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
*equality replacement requirements