Show the Proof¶

In [1]:

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

Out[1]:

	step type	requirements	statement
0	instantiation	1, 2, 3	⊢
	: , :
1	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
2	instantiation	5, 4	⊢
	:
3	instantiation	5, 6	⊢
	:
4	instantiation	9, 10, 7, 8	⊢
	: , :
5	theorem		⊢
	proveit.numbers.negation.real_closure
6	instantiation	9, 10, 11, 12	⊢
	: , :
7	instantiation	16, 39, 26	⊢
	: , :
8	instantiation	19, 77, 13, 14, 30	⊢
	: , :
9	theorem		⊢
	proveit.numbers.division.div_real_closure
10	instantiation	84, 45, 15	⊢
	: , : , :
11	instantiation	16, 17, 18	⊢
	: , :
12	instantiation	19, 77, 20, 21, 22	⊢
	: , :
13	instantiation	27	⊢
	: , :
14	instantiation	84, 36, 23	⊢
	: , : , :
15	instantiation	84, 51, 63	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
17	instantiation	84, 45, 24	⊢
	: , : , :
18	instantiation	25, 26, 77	⊢
	: , :
19	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
20	instantiation	27	⊢
	: , :
21	instantiation	84, 36, 28	⊢
	: , : , :
22	instantiation	29, 30, 31	⊢
	: , :
23	instantiation	84, 43, 32	⊢
	: , : , :
24	instantiation	84, 51, 33	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
26	instantiation	84, 45, 34	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
28	instantiation	84, 43, 35	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_nonzero_closure
30	instantiation	84, 36, 37	⊢
	: , : , :
31	instantiation	84, 38, 39	⊢
	: , : , :
32	instantiation	84, 49, 40	⊢
	: , : , :
33	instantiation	84, 76, 41	⊢
	: , : , :
34	instantiation	84, 51, 55	⊢
	: , : , :
35	instantiation	84, 49, 42	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
37	instantiation	84, 43, 44	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
39	instantiation	84, 45, 46	⊢
	: , : , :
40	instantiation	84, 52, 47	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
42	instantiation	84, 52, 48	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
44	instantiation	84, 49, 50	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
46	instantiation	84, 51, 72	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
48	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
49	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
50	instantiation	84, 52, 53	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
52	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
53	instantiation	54, 55, 56	⊢
	:
54	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
55	instantiation	84, 57, 65	⊢
	: , : , :
56	instantiation	58, 59, 60	⊢
	: , : , :
57	instantiation	61, 63, 64	⊢
	: , :
58	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
59	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
60	instantiation	62, 63, 64, 65	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
62	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
63	instantiation	84, 76, 66	⊢
	: , : , :
64	instantiation	78, 67, 68	⊢
	: , :
65	theorem		⊢
	proveit.physics.quantum.QPE._e_value_in_e_domain
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
67	instantiation	69, 72, 70	⊢
	: , :
68	instantiation	71, 72	⊢
	:
69	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
70	instantiation	73, 74, 75	⊢
	:
71	theorem		⊢
	proveit.numbers.negation.int_closure
72	instantiation	84, 76, 77	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
74	instantiation	78, 79, 80	⊢
	: , :
75	instantiation	81, 82	⊢
	: , :
76	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
77	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
78	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
79	instantiation	84, 83, 88	⊢
	: , : , :
80	instantiation	84, 85, 86	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.addition.subtraction.nonneg_difference
82	instantiation	87, 88	⊢
	:
83	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
84	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
85	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
86	instantiation	89, 90	⊢
	:
87	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
88	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
89	theorem		⊢
	proveit.numbers.negation.int_neg_closure
90	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1