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