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.leftward_commutation
2	reference	68	⊢
3	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
4	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
5	instantiation	76, 8, 7	⊢
	: , : , :
6	instantiation	76, 8, 9	⊢
	: , : , :
7	modus ponens	10, 11	⊢
8	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
9	instantiation	18, 19, 12, 13	⊢
	: , :
10	instantiation	14	⊢
	: , : , :
11	generalization	15	⊢
12	instantiation	25, 16, 78	⊢
	: , :
13	instantiation	27, 17, 29	⊢
	: , :
14	theorem		⊢
	proveit.numbers.summation.summation_real_closure
15	instantiation	18, 19, 20, 21	,  ⊢
	: , :
16	instantiation	76, 30, 22	⊢
	: , : , :
17	instantiation	76, 33, 23	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.division.div_real_closure
19	instantiation	76, 30, 24	⊢
	: , : , :
20	instantiation	25, 26, 78	,  ⊢
	: , :
21	instantiation	27, 28, 29	,  ⊢
	: , :
22	instantiation	76, 35, 53	⊢
	: , : , :
23	instantiation	76, 37, 50	⊢
	: , : , :
24	instantiation	76, 35, 65	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
26	instantiation	76, 30, 31	,  ⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
28	instantiation	76, 33, 32	,  ⊢
	: , : , :
29	instantiation	76, 33, 34	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
31	instantiation	76, 35, 39	,  ⊢
	: , : , :
32	instantiation	76, 37, 36	,  ⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
34	instantiation	76, 37, 38	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
36	instantiation	52, 39, 40	,  ⊢
	:
37	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
38	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
39	instantiation	76, 41, 48	,  ⊢
	: , : , :
40	instantiation	58, 42, 43	,  ⊢
	: , : , :
41	instantiation	63, 46, 47	⊢
	: , :
42	instantiation	44, 45	⊢
	:
43	instantiation	64, 46, 47, 48	,  ⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
45	instantiation	49, 50, 62	⊢
	: , :
46	instantiation	69, 53, 65	⊢
	: , :
47	instantiation	69, 70, 51	⊢
	: , :
48	assumption		⊢
49	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
50	instantiation	52, 53, 54	⊢
	:
51	instantiation	76, 55, 56	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
53	instantiation	76, 57, 67	⊢
	: , : , :
54	instantiation	58, 59, 60	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
56	instantiation	61, 62	⊢
	:
57	instantiation	63, 65, 66	⊢
	: , :
58	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
59	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
60	instantiation	64, 65, 66, 67	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.negation.int_neg_closure
62	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
63	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
64	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
65	instantiation	76, 77, 68	⊢
	: , : , :
66	instantiation	69, 70, 71	⊢
	: , :
67	assumption		⊢
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
69	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
70	instantiation	76, 72, 73	⊢
	: , : , :
71	instantiation	74, 75	⊢
	:
72	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
73	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
74	theorem		⊢
	proveit.numbers.negation.int_closure
75	instantiation	76, 77, 78	⊢
	: , : , :
76	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
77	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
78	theorem		⊢
	proveit.numbers.numerals.decimals.nat2