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