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	reference	60	⊢
2	instantiation	51, 4	⊢
	: , : , :
3	instantiation	5, 103, 93, 6*	⊢
	: , : , : , :
4	instantiation	7, 8, 9, 10, 11*	⊢
	: , :
5	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
6	instantiation	60, 12, 13	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.division.div_as_mult
8	instantiation	104, 82, 14	⊢
	: , : , :
9	instantiation	104, 82, 15	⊢
	: , : , :
10	instantiation	47, 26	⊢
	:
11	instantiation	60, 16, 17	⊢
	: , : , :
12	instantiation	41, 99, 18, 19, 20, 21	⊢
	: , : , : , :
13	instantiation	22, 23, 24	⊢
	:
14	instantiation	94, 95, 25	⊢
	: , : , :
15	instantiation	94, 95, 26	⊢
	: , : , :
16	instantiation	51, 27	⊢
	: , : , :
17	instantiation	28, 66, 29, 81, 36, 30*	⊢
	: , : , :
18	instantiation	80	⊢
	: , :
19	instantiation	80	⊢
	: , :
20	instantiation	60, 31, 32	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
22	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
23	instantiation	104, 82, 33	⊢
	: , : , :
24	instantiation	47, 34	⊢
	:
25	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
26	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
27	instantiation	35, 66, 88, 83, 36, 37*	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
29	instantiation	38, 88, 83	⊢
	: , :
30	instantiation	60, 39, 40	⊢
	: , : , :
31	instantiation	41, 99, 42, 43, 44, 45	⊢
	: , : , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
33	instantiation	104, 97, 46	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
35	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
36	instantiation	47, 92	⊢
	:
37	instantiation	48, 74, 49, 50*	⊢
	: , :
38	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
39	instantiation	51, 52	⊢
	: , : , :
40	instantiation	53, 54, 55, 56*	⊢
	: , :
41	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
42	instantiation	80	⊢
	: , :
43	instantiation	80	⊢
	: , :
44	instantiation	57, 66	⊢
	:
45	instantiation	59, 66	⊢
	:
46	instantiation	104, 102, 58	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
48	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
49	instantiation	104, 82, 90	⊢
	: , : , :
50	instantiation	59, 74	⊢
	:
51	axiom		⊢
	proveit.logic.equality.substitution
52	instantiation	60, 61, 62	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
54	instantiation	104, 63, 64	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
56	instantiation	65, 66	⊢
	:
57	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
58	instantiation	104, 105, 67	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
60	axiom		⊢
	proveit.logic.equality.equals_transitivity
61	instantiation	68, 69, 99, 106, 70, 71, 74, 75, 72	⊢
	: , : , : , : , : , :
62	instantiation	73, 74, 75, 76	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
64	instantiation	104, 77, 78	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
66	instantiation	104, 82, 79	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
68	theorem		⊢
	proveit.numbers.addition.disassociation
69	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
70	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
71	instantiation	80	⊢
	: , :
72	instantiation	104, 82, 81	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
74	instantiation	104, 82, 88	⊢
	: , : , :
75	instantiation	104, 82, 83	⊢
	: , : , :
76	instantiation	84	⊢
	:
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
78	instantiation	104, 85, 86	⊢
	: , : , :
79	instantiation	104, 97, 87	⊢
	: , : , :
80	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
81	instantiation	89, 88	⊢
	:
82	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
83	instantiation	89, 90	⊢
	:
84	axiom		⊢
	proveit.logic.equality.equals_reflexivity
85	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
86	instantiation	104, 91, 92	⊢
	: , : , :
87	instantiation	104, 102, 93	⊢
	: , : , :
88	instantiation	94, 95, 96	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.negation.real_closure
90	instantiation	104, 97, 98	⊢
	: , : , :
91	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
92	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
93	instantiation	104, 105, 99	⊢
	: , : , :
94	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
95	instantiation	100, 101	⊢
	: , :
96	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
97	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
98	instantiation	104, 102, 103	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
100	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
101	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
102	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
103	instantiation	104, 105, 106	⊢
	: , : , :
104	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
105	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
106	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements