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	⊢
	: , : , : , : , :
1	theorem		⊢
	proveit.logic.sets.enumeration.proper_subset_of_superset
2	reference	70	⊢
3	reference	66	⊢
4	reference	7	⊢
5	instantiation	6, 70, 7, 8, 9, 10	⊢
	: , : , :
6	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
7	instantiation	11	⊢
	: , : , :
8	instantiation	14, 12	⊢
	: , :
9	instantiation	14, 13	⊢
	: , :
10	instantiation	14, 15	⊢
	: , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
12	instantiation	18, 66, 19, 16	⊢
	: , :
13	instantiation	18, 67, 19, 17	⊢
	: , :
14	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
15	instantiation	18, 70, 19, 20	⊢
	: , :
16	instantiation	28, 54, 29, 21, 22, 23^, 24^	⊢
	: , : , :
17	instantiation	28, 55, 29, 57, 25, 26^, 27^	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
19	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
20	instantiation	28, 57, 29, 55, 30, 31^, 39^	⊢
	: , : , :
21	instantiation	68, 60, 32	⊢
	: , : , :
22	instantiation	41, 33	⊢
	:
23	instantiation	43, 34, 35	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
25	instantiation	41, 36	⊢
	:
26	instantiation	43, 37, 38	⊢
	: , : , :
27	instantiation	43, 39, 40	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
30	instantiation	41, 42	⊢
	:
31	instantiation	43, 44, 45	⊢
	: , : , :
32	instantiation	68, 64, 46	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
34	instantiation	49, 47	⊢
	:
35	instantiation	50, 47, 52	⊢
	: , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
37	instantiation	49, 48	⊢
	:
38	instantiation	50, 48, 52	⊢
	: , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
40	instantiation	50, 48, 51	⊢
	: , :
41	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
42	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
43	theorem		⊢
	proveit.logic.equality.sub_right_side_into
44	instantiation	49, 51	⊢
	:
45	instantiation	50, 51, 52	⊢
	: , :
46	instantiation	68, 69, 53	⊢
	: , : , :
47	instantiation	68, 56, 54	⊢
	: , : , :
48	instantiation	68, 56, 55	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.addition.elim_zero_right
50	theorem		⊢
	proveit.numbers.addition.commutation
51	instantiation	68, 56, 57	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
54	instantiation	68, 60, 58	⊢
	: , : , :
55	instantiation	68, 60, 59	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
57	instantiation	68, 60, 61	⊢
	: , : , :
58	instantiation	68, 64, 62	⊢
	: , : , :
59	instantiation	68, 64, 63	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
61	instantiation	68, 64, 65	⊢
	: , : , :
62	instantiation	68, 69, 66	⊢
	: , : , :
63	instantiation	68, 69, 67	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
65	instantiation	68, 69, 70	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
68	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
^*equality replacement requirements