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	13	⊢
2	instantiation	4, 5	⊢
	: , :
3	instantiation	6, 65, 7, 8	⊢
	: , : , :
4	theorem		⊢
	proveit.logic.sets.membership.unfold_not_in_set
5	instantiation	9, 65, 10, 11, 12	⊢
	: , : , :
6	theorem		⊢
	proveit.logic.sets.enumeration.fold
7	instantiation	16	⊢
	: , :
8	instantiation	13, 14, 15	⊢
	: , :
9	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
10	instantiation	16	⊢
	: , :
11	instantiation	27, 17	⊢
	: , :
12	instantiation	18, 19, 31	⊢
	: , : , :
13	theorem		⊢
	proveit.logic.booleans.disjunction.or_if_only_right
14	instantiation	20, 21	⊢
	: , :
15	instantiation	22, 23	⊢
	: , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
17	instantiation	32, 65, 64, 24	⊢
	: , :
18	theorem		⊢
	proveit.logic.equality.sub_left_side_into
19	instantiation	32, 64, 25, 26	⊢
	: , :
20	theorem		⊢
	proveit.logic.equality.unfold_not_equals
21	instantiation	27, 28	⊢
	: , :
22	theorem		⊢
	proveit.logic.equality.equals_reversal
23	instantiation	47, 42, 29	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
25	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
26	instantiation	38, 50, 39, 51, 40, 30^, 31^	⊢
	: , : , :
27	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
28	instantiation	32, 70, 64, 33	⊢
	: , :
29	instantiation	53, 44, 54	⊢
	: , :
30	instantiation	47, 34, 35	⊢
	: , : , :
31	instantiation	47, 36, 37	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
33	instantiation	38, 59, 39, 51, 40, 41^, 42^	⊢
	: , : , :
34	instantiation	52, 43	⊢
	:
35	instantiation	53, 43, 55	⊢
	: , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_2
37	instantiation	53, 43, 44	⊢
	: , :
38	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
40	instantiation	45, 46	⊢
	:
41	instantiation	47, 48, 49	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
43	instantiation	68, 58, 50	⊢
	: , : , :
44	instantiation	68, 58, 51	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
47	theorem		⊢
	proveit.logic.equality.sub_right_side_into
48	instantiation	52, 54	⊢
	:
49	instantiation	53, 54, 55	⊢
	: , :
50	instantiation	68, 62, 56	⊢
	: , : , :
51	instantiation	68, 62, 57	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.addition.elim_zero_right
53	theorem		⊢
	proveit.numbers.addition.commutation
54	instantiation	68, 58, 59	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
56	instantiation	68, 66, 60	⊢
	: , : , :
57	instantiation	68, 66, 61	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
59	instantiation	68, 62, 63	⊢
	: , : , :
60	instantiation	68, 69, 64	⊢
	: , : , :
61	instantiation	68, 69, 65	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
63	instantiation	68, 66, 67	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
65	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
66	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
67	instantiation	68, 69, 70	⊢
	: , : , :
68	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements