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.equality.unfold_not_equals
2	instantiation	3, 63, 4	⊢
	: , : , : , : , :
3	theorem		⊢
	proveit.logic.booleans.conjunction.any_from_and
4	instantiation	5, 62, 6, 7	⊢
	: , : , :
5	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_unfold
6	instantiation	19	⊢
	: , : , :
7	instantiation	8, 9, 10	⊢
	: , : , :
8	theorem		⊢
	proveit.logic.equality.sub_left_side_into
9	instantiation	11, 62, 12, 13, 14, 15	⊢
	: , : , :
10	instantiation	16, 17, 18	⊢
	: , : , :
11	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
12	instantiation	19	⊢
	: , : , :
13	instantiation	20, 21	⊢
	: , :
14	instantiation	30, 66, 62, 22	⊢
	: , :
15	instantiation	30, 66, 23, 24	⊢
	: , :
16	axiom		⊢
	proveit.logic.equality.equals_transitivity
17	instantiation	25, 26	⊢
	: , : , :
18	instantiation	27, 63, 28, 29	⊢
	: , : , : , : , : , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
20	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
21	instantiation	30, 63, 66, 31	⊢
	: , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
23	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
24	instantiation	32, 53, 33, 34, 35^, 36^	⊢
	: , : , :
25	axiom		⊢
	proveit.logic.equality.substitution
26	instantiation	41, 37, 38	⊢
	: , : , :
27	theorem		⊢
	proveit.logic.sets.enumeration.leftward_permutation
28	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
29	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
30	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
31	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
32	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
34	instantiation	39, 40	⊢
	:
35	instantiation	41, 42, 43	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
37	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
38	instantiation	47, 44, 45	⊢
	: , :
39	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
40	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
41	theorem		⊢
	proveit.logic.equality.sub_right_side_into
42	instantiation	46, 48	⊢
	:
43	instantiation	47, 48, 49	⊢
	: , :
44	instantiation	64, 52, 50	⊢
	: , : , :
45	instantiation	64, 52, 51	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.addition.elim_zero_right
47	theorem		⊢
	proveit.numbers.addition.commutation
48	instantiation	64, 52, 53	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
50	instantiation	64, 56, 54	⊢
	: , : , :
51	instantiation	64, 56, 55	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
53	instantiation	64, 56, 57	⊢
	: , : , :
54	instantiation	64, 60, 58	⊢
	: , : , :
55	instantiation	64, 60, 59	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
57	instantiation	64, 60, 61	⊢
	: , : , :
58	instantiation	64, 65, 62	⊢
	: , : , :
59	instantiation	64, 65, 63	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
61	instantiation	64, 65, 66	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
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