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	⊢
	: , : , :
1	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
2	reference	69	⊢
3	instantiation	7	⊢
	: , : , :
4	instantiation	10, 8	⊢
	: , :
5	instantiation	10, 9	⊢
	: , :
6	instantiation	10, 11	⊢
	: , :
7	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
8	instantiation	14, 65, 15, 12	⊢
	: , :
9	instantiation	14, 66, 15, 13	⊢
	: , :
10	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
11	instantiation	14, 69, 15, 16	⊢
	: , :
12	instantiation	25, 52, 26, 17, 18, 19^, 20^	⊢
	: , : , :
13	instantiation	25, 54, 26, 21, 22, 23^, 24^	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
15	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
16	instantiation	25, 56, 26, 27, 28^, 29^	⊢
	: , : , :
17	instantiation	67, 59, 30	⊢
	: , : , :
18	instantiation	38, 31	⊢
	:
19	instantiation	40, 32, 33	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.add_5_1
21	instantiation	67, 59, 34	⊢
	: , : , :
22	instantiation	38, 35	⊢
	:
23	instantiation	40, 36, 37	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_2
25	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
27	instantiation	38, 39	⊢
	:
28	instantiation	40, 41, 42	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_3
30	instantiation	67, 63, 43	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.posnat5
32	instantiation	47, 44	⊢
	:
33	instantiation	48, 44, 50	⊢
	: , :
34	instantiation	67, 63, 45	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
36	instantiation	47, 46	⊢
	:
37	instantiation	48, 46, 50	⊢
	: , :
38	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
40	theorem		⊢
	proveit.logic.equality.sub_right_side_into
41	instantiation	47, 49	⊢
	:
42	instantiation	48, 49, 50	⊢
	: , :
43	instantiation	67, 68, 51	⊢
	: , : , :
44	instantiation	67, 55, 52	⊢
	: , : , :
45	instantiation	67, 68, 53	⊢
	: , : , :
46	instantiation	67, 55, 54	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.addition.elim_zero_right
48	theorem		⊢
	proveit.numbers.addition.commutation
49	instantiation	67, 55, 56	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
52	instantiation	67, 59, 57	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
54	instantiation	67, 59, 58	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
56	instantiation	67, 59, 60	⊢
	: , : , :
57	instantiation	67, 63, 61	⊢
	: , : , :
58	instantiation	67, 63, 62	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
60	instantiation	67, 63, 64	⊢
	: , : , :
61	instantiation	67, 68, 65	⊢
	: , : , :
62	instantiation	67, 68, 66	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
64	instantiation	67, 68, 69	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
67	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
^*equality replacement requirements