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	4	⊢
2	instantiation	4, 5, 6	⊢
	: , : , :
3	instantiation	20, 7, 8	⊢
	: , : , :
4	theorem		⊢
	proveit.logic.equality.sub_right_side_into
5	instantiation	9, 23, 10, 11, 12	⊢
	: , : , : , : , :
6	instantiation	30, 13	⊢
	: , : , :
7	instantiation	30, 14	⊢
	: , : , :
8	instantiation	39, 15	⊢
	:
9	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
10	instantiation	63, 18, 16	⊢
	: , : , :
11	instantiation	63, 18, 17	⊢
	: , : , :
12	instantiation	63, 18, 19	⊢
	: , : , :
13	instantiation	20, 21, 22	⊢
	: , : , :
14	instantiation	32, 23	⊢
	:
15	instantiation	63, 46, 24	⊢
	: , : , :
16	instantiation	63, 26, 25	⊢
	: , : , :
17	instantiation	63, 26, 27	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
19	instantiation	63, 28, 29	⊢
	: , : , :
20	axiom		⊢
	proveit.logic.equality.equals_transitivity
21	instantiation	30, 31	⊢
	: , : , :
22	instantiation	32, 40	⊢
	:
23	instantiation	63, 46, 55	⊢
	: , : , :
24	instantiation	33, 55, 49, 34	⊢
	: , :
25	instantiation	63, 36, 35	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
27	instantiation	63, 36, 37	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
29	instantiation	38, 49, 50	⊢
	:
30	axiom		⊢
	proveit.logic.equality.substitution
31	instantiation	39, 40	⊢
	:
32	theorem		⊢
	proveit.numbers.division.frac_one_denom
33	theorem		⊢
	proveit.numbers.division.div_real_closure
34	instantiation	41, 42	⊢
	: , :
35	instantiation	63, 44, 43	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
37	instantiation	63, 44, 45	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
39	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
40	instantiation	63, 46, 47	⊢
	: , : , :
41	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
42	instantiation	48, 54, 49, 50	⊢
	: , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
45	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
47	instantiation	63, 58, 51	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
49	instantiation	52, 54, 55, 56	⊢
	: , : , :
50	instantiation	53, 54, 55, 56	⊢
	: , : , :
51	instantiation	63, 61, 57	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
55	instantiation	63, 58, 59	⊢
	: , : , :
56	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
57	instantiation	63, 64, 60	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
59	instantiation	63, 61, 62	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
61	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
62	instantiation	63, 64, 65	⊢
	: , : , :
63	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
64	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
65	theorem		⊢
	proveit.numbers.numerals.decimals.nat1