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.logic.equality.sub_left_side_into
2	instantiation	4, 43, 5, 6	⊢
	: , : , :
3	assumption		⊢
4	theorem		⊢
	proveit.logic.sets.intersection.nonmembership_folding
5	instantiation	7	⊢
	: , :
6	instantiation	8, 9, 10	⊢
	: , :
7	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
8	theorem		⊢
	proveit.logic.booleans.disjunction.or_if_only_left
9	instantiation	11, 53, 22, 12, 13, 14	⊢
	: , : , :
10	instantiation	15, 16	⊢
	: , :
11	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
12	instantiation	19, 17	⊢
	: , :
13	instantiation	19, 18	⊢
	: , :
14	instantiation	19, 20	⊢
	: , :
15	theorem		⊢
	proveit.logic.sets.membership.double_negated_membership
16	instantiation	21, 53, 63, 22	⊢
	: , : , : , : , :
17	instantiation	25, 63, 26, 23	⊢
	: , :
18	instantiation	25, 66, 26, 24	⊢
	: , :
19	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
20	instantiation	25, 53, 26, 27	⊢
	: , :
21	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
22	instantiation	28	⊢
	: , : , :
23	instantiation	33, 54, 34, 29, 30, 31^, 32^	⊢
	: , : , :
24	instantiation	33, 56, 34, 35, 36^, 37^	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
26	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
27	theorem		⊢
	proveit.numbers.numerals.decimals.less_3_4
28	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
29	instantiation	64, 58, 38	⊢
	: , : , :
30	instantiation	42, 39	⊢
	:
31	instantiation	44, 40, 41	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
33	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
35	instantiation	42, 43	⊢
	:
36	instantiation	44, 45, 46	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
38	instantiation	64, 61, 47	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
40	instantiation	49, 48	⊢
	:
41	instantiation	50, 48, 52	⊢
	: , :
42	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
43	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
44	theorem		⊢
	proveit.logic.equality.sub_right_side_into
45	instantiation	49, 51	⊢
	:
46	instantiation	50, 51, 52	⊢
	: , :
47	instantiation	64, 65, 53	⊢
	: , : , :
48	instantiation	64, 55, 54	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.addition.elim_zero_right
50	theorem		⊢
	proveit.numbers.addition.commutation
51	instantiation	64, 55, 56	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
54	instantiation	64, 58, 57	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
56	instantiation	64, 58, 59	⊢
	: , : , :
57	instantiation	64, 61, 60	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
59	instantiation	64, 61, 62	⊢
	: , : , :
60	instantiation	64, 65, 63	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
62	instantiation	64, 65, 66	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
64	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
65	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements