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.addition.weak_bound_via_right_term_bound
2	instantiation	121, 18	⊢
	:
3	instantiation	121, 19	⊢
	:
4	instantiation	121, 8	⊢
	:
5	instantiation	7, 8, 19, 9	⊢
	: , :
6	instantiation	10, 11, 12, 79, 13	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.negation.negated_weak_bound
8	instantiation	25, 15, 40, 33	⊢
	: , :
9	instantiation	14, 40, 15, 39, 16, 17	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.addition.subtraction.negated_add
11	instantiation	136, 114, 18	⊢
	: , : , :
12	instantiation	136, 114, 19	⊢
	: , : , :
13	instantiation	92, 20, 21	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.division.weak_div_from_numer_bound__pos_denom
15	instantiation	136, 129, 22	⊢
	: , : , :
16	instantiation	23, 51, 76, 38	⊢
	: , : , :
17	instantiation	24, 52	⊢
	:
18	instantiation	25, 122, 111, 64	⊢
	: , :
19	instantiation	25, 39, 40, 33	⊢
	: , :
20	instantiation	81, 26	⊢
	: , : , :
21	instantiation	27, 135, 125, 28*	⊢
	: , : , : , :
22	instantiation	136, 134, 29	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
24	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
25	theorem		⊢
	proveit.numbers.division.div_real_closure
26	instantiation	30, 31, 32, 33, 34*	⊢
	: , :
27	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
28	instantiation	92, 35, 36	⊢
	: , : , :
29	instantiation	136, 37, 38	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.division.div_as_mult
31	instantiation	136, 114, 39	⊢
	: , : , :
32	instantiation	136, 114, 40	⊢
	: , : , :
33	instantiation	77, 52	⊢
	:
34	instantiation	92, 41, 42	⊢
	: , : , :
35	instantiation	69, 131, 43, 44, 45, 46	⊢
	: , : , : , :
36	instantiation	47, 48, 49	⊢
	:
37	instantiation	50, 51, 76	⊢
	: , :
38	assumption		⊢
39	instantiation	126, 127, 90	⊢
	: , : , :
40	instantiation	126, 127, 52	⊢
	: , : , :
41	instantiation	81, 53	⊢
	: , : , :
42	instantiation	54, 98, 55, 113, 64, 56*	⊢
	: , : , :
43	instantiation	112	⊢
	: , :
44	instantiation	112	⊢
	: , :
45	instantiation	92, 57, 58	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
47	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
48	instantiation	136, 114, 59	⊢
	: , : , :
49	instantiation	77, 60	⊢
	:
50	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
51	instantiation	61, 62, 135	⊢
	: , :
52	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
53	instantiation	63, 98, 120, 115, 64, 65*	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
55	instantiation	66, 120, 115	⊢
	: , :
56	instantiation	92, 67, 68	⊢
	: , : , :
57	instantiation	69, 131, 70, 71, 72, 73	⊢
	: , : , : , :
58	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
59	instantiation	136, 129, 74	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
61	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
62	instantiation	75, 76	⊢
	:
63	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_real_power
64	instantiation	77, 124	⊢
	:
65	instantiation	78, 106, 79, 80*	⊢
	: , :
66	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
67	instantiation	81, 82	⊢
	: , : , :
68	instantiation	83, 84, 85, 86*	⊢
	: , :
69	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
70	instantiation	112	⊢
	: , :
71	instantiation	112	⊢
	: , :
72	instantiation	87, 98	⊢
	:
73	instantiation	91, 98	⊢
	:
74	instantiation	136, 134, 88	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.negation.int_closure
76	instantiation	136, 89, 90	⊢
	: , : , :
77	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
78	theorem		⊢
	proveit.numbers.multiplication.mult_neg_right
79	instantiation	136, 114, 122	⊢
	: , : , :
80	instantiation	91, 106	⊢
	:
81	axiom		⊢
	proveit.logic.equality.substitution
82	instantiation	92, 93, 94	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
84	instantiation	136, 95, 96	⊢
	: , : , :
85	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
86	instantiation	97, 98	⊢
	:
87	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
88	instantiation	136, 137, 99	⊢
	: , : , :
89	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
90	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
91	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
92	axiom		⊢
	proveit.logic.equality.equals_transitivity
93	instantiation	100, 101, 131, 138, 102, 103, 106, 107, 104	⊢
	: , : , : , : , : , :
94	instantiation	105, 106, 107, 108	⊢
	: , : , :
95	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
96	instantiation	136, 109, 110	⊢
	: , : , :
97	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
98	instantiation	136, 114, 111	⊢
	: , : , :
99	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
100	theorem		⊢
	proveit.numbers.addition.disassociation
101	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
102	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
103	instantiation	112	⊢
	: , :
104	instantiation	136, 114, 113	⊢
	: , : , :
105	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
106	instantiation	136, 114, 120	⊢
	: , : , :
107	instantiation	136, 114, 115	⊢
	: , : , :
108	instantiation	116	⊢
	:
109	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
110	instantiation	136, 117, 118	⊢
	: , : , :
111	instantiation	136, 129, 119	⊢
	: , : , :
112	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
113	instantiation	121, 120	⊢
	:
114	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
115	instantiation	121, 122	⊢
	:
116	axiom		⊢
	proveit.logic.equality.equals_reflexivity
117	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
118	instantiation	136, 123, 124	⊢
	: , : , :
119	instantiation	136, 134, 125	⊢
	: , : , :
120	instantiation	126, 127, 128	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.negation.real_closure
122	instantiation	136, 129, 130	⊢
	: , : , :
123	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
124	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
125	instantiation	136, 137, 131	⊢
	: , : , :
126	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
127	instantiation	132, 133	⊢
	: , :
128	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
129	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
130	instantiation	136, 134, 135	⊢
	: , : , :
131	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
132	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
133	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
134	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
135	instantiation	136, 137, 138	⊢
	: , : , :
136	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
137	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
138	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
*equality replacement requirements