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	66	⊢
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, 62, 15, 12	⊢
	: , :
9	instantiation	14, 63, 15, 13	⊢
	: , :
10	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
11	instantiation	14, 66, 15, 16	⊢
	: , :
12	instantiation	24, 50, 25, 17, 18, 19^, 20^	⊢
	: , : , :
13	instantiation	24, 51, 25, 53, 21, 22^, 23^	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
15	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
16	instantiation	24, 53, 25, 51, 26, 27^, 35^	⊢
	: , : , :
17	instantiation	64, 56, 28	⊢
	: , : , :
18	instantiation	37, 29	⊢
	:
19	instantiation	39, 30, 31	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
21	instantiation	37, 32	⊢
	:
22	instantiation	39, 33, 34	⊢
	: , : , :
23	instantiation	39, 35, 36	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
26	instantiation	37, 38	⊢
	:
27	instantiation	39, 40, 41	⊢
	: , : , :
28	instantiation	64, 60, 42	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
30	instantiation	45, 43	⊢
	:
31	instantiation	46, 43, 48	⊢
	: , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
33	instantiation	45, 44	⊢
	:
34	instantiation	46, 44, 48	⊢
	: , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
36	instantiation	46, 44, 47	⊢
	: , :
37	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
38	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
39	theorem		⊢
	proveit.logic.equality.sub_right_side_into
40	instantiation	45, 47	⊢
	:
41	instantiation	46, 47, 48	⊢
	: , :
42	instantiation	64, 65, 49	⊢
	: , : , :
43	instantiation	64, 52, 50	⊢
	: , : , :
44	instantiation	64, 52, 51	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.addition.elim_zero_right
46	theorem		⊢
	proveit.numbers.addition.commutation
47	instantiation	64, 52, 53	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
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.nat1
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
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.nat3
^*equality replacement requirements