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.sets.subtraction.membership_folding
2	instantiation	4, 5, 6, 7	⊢
	: , : , :
3	instantiation	8, 9, 24	⊢
	: , : , :
4	theorem		⊢
	proveit.logic.sets.enumeration.fold
5	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
6	instantiation	10	⊢
	: , : , : , : , :
7	instantiation	11, 60, 70, 12, 13, 14, 15, 16, 17, 24	⊢
	: , : , : , : , :
8	theorem		⊢
	proveit.logic.equality.sub_left_side_into
9	instantiation	18, 60, 19, 20, 21, 22	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_5_typical_eq
11	theorem		⊢
	proveit.logic.booleans.disjunction.or_if_any
12	instantiation	26	⊢
	: , : , :
13	instantiation	25	⊢
	: , :
14	instantiation	25	⊢
	: , :
15	instantiation	25	⊢
	: , :
16	instantiation	23, 24	⊢
	:
17	instantiation	25	⊢
	: , :
18	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
19	instantiation	26	⊢
	: , : , :
20	instantiation	29, 27	⊢
	: , :
21	instantiation	29, 28	⊢
	: , :
22	instantiation	29, 30	⊢
	: , :
23	theorem		⊢
	proveit.logic.booleans.in_bool_if_true
24	assumption		⊢
25	axiom		⊢
	proveit.logic.equality.equality_in_bool
26	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
27	instantiation	33, 70, 34, 31	⊢
	: , :
28	instantiation	33, 73, 34, 32	⊢
	: , :
29	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
30	instantiation	33, 60, 34, 35	⊢
	: , :
31	instantiation	40, 61, 41, 36, 37, 38^, 39^	⊢
	: , : , :
32	instantiation	40, 63, 41, 42, 43^, 44^	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
34	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
35	theorem		⊢
	proveit.numbers.numerals.decimals.less_3_4
36	instantiation	71, 65, 45	⊢
	: , : , :
37	instantiation	49, 46	⊢
	:
38	instantiation	51, 47, 48	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
40	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
42	instantiation	49, 50	⊢
	:
43	instantiation	51, 52, 53	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
45	instantiation	71, 68, 54	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
47	instantiation	56, 55	⊢
	:
48	instantiation	57, 55, 59	⊢
	: , :
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	56, 58	⊢
	:
53	instantiation	57, 58, 59	⊢
	: , :
54	instantiation	71, 72, 60	⊢
	: , : , :
55	instantiation	71, 62, 61	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.addition.elim_zero_right
57	theorem		⊢
	proveit.numbers.addition.commutation
58	instantiation	71, 62, 63	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
60	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
61	instantiation	71, 65, 64	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
63	instantiation	71, 65, 66	⊢
	: , : , :
64	instantiation	71, 68, 67	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
66	instantiation	71, 68, 69	⊢
	: , : , :
67	instantiation	71, 72, 70	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
69	instantiation	71, 72, 73	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
71	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
72	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements