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, 4, 5, 6, 7, 8	⊢
	: , : , :
1	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
2	reference	62	⊢
3	instantiation	9	⊢
	: , : , : , : , :
4	instantiation	14, 10	⊢
	: , :
5	instantiation	14, 11	⊢
	: , :
6	instantiation	14, 12	⊢
	: , :
7	instantiation	14, 13	⊢
	: , :
8	instantiation	14, 15	⊢
	: , :
9	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
10	instantiation	20, 78, 21, 16	⊢
	: , :
11	instantiation	20, 79, 21, 17	⊢
	: , :
12	instantiation	20, 80, 21, 18	⊢
	: , :
13	instantiation	20, 83, 21, 19	⊢
	: , :
14	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
15	instantiation	20, 62, 21, 22	⊢
	: , :
16	instantiation	33, 63, 34, 23, 24, 25^, 26^	⊢
	: , : , :
17	instantiation	33, 64, 34, 67, 27, 28^, 29^	⊢
	: , : , :
18	instantiation	33, 65, 34, 30, 31^, 32^	⊢
	: , : , :
19	instantiation	33, 67, 34, 64, 35, 36^, 44^	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
21	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
22	theorem		⊢
	proveit.numbers.numerals.decimals.less_5_6
23	instantiation	81, 71, 37	⊢
	: , : , :
24	instantiation	49, 38	⊢
	:
25	instantiation	51, 39, 40	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.add_5_1
27	instantiation	49, 41	⊢
	:
28	instantiation	51, 42, 43	⊢
	: , : , :
29	instantiation	51, 44, 45	⊢
	: , : , :
30	instantiation	49, 46	⊢
	:
31	instantiation	51, 47, 48	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_3
33	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
35	instantiation	49, 50	⊢
	:
36	instantiation	51, 52, 53	⊢
	: , : , :
37	instantiation	81, 76, 54	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
39	instantiation	58, 55	⊢
	:
40	instantiation	59, 55, 61	⊢
	: , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
42	instantiation	58, 56	⊢
	:
43	instantiation	59, 56, 61	⊢
	: , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_4
45	instantiation	59, 56, 60	⊢
	: , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
47	instantiation	58, 57	⊢
	:
48	instantiation	59, 57, 61	⊢
	: , :
49	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
50	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
51	theorem		⊢
	proveit.logic.equality.sub_right_side_into
52	instantiation	58, 60	⊢
	:
53	instantiation	59, 60, 61	⊢
	: , :
54	instantiation	81, 82, 62	⊢
	: , : , :
55	instantiation	81, 66, 63	⊢
	: , : , :
56	instantiation	81, 66, 64	⊢
	: , : , :
57	instantiation	81, 66, 65	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.addition.elim_zero_right
59	theorem		⊢
	proveit.numbers.addition.commutation
60	instantiation	81, 66, 67	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
63	instantiation	81, 71, 68	⊢
	: , : , :
64	instantiation	81, 71, 69	⊢
	: , : , :
65	instantiation	81, 71, 70	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
67	instantiation	81, 71, 72	⊢
	: , : , :
68	instantiation	81, 76, 73	⊢
	: , : , :
69	instantiation	81, 76, 74	⊢
	: , : , :
70	instantiation	81, 76, 75	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
72	instantiation	81, 76, 77	⊢
	: , : , :
73	instantiation	81, 82, 78	⊢
	: , : , :
74	instantiation	81, 82, 79	⊢
	: , : , :
75	instantiation	81, 82, 80	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
77	instantiation	81, 82, 83	⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
79	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
81	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
82	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
83	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
^*equality replacement requirements