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