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, 7^*	⊢
	: , : , : , : , :
1	theorem		⊢
	proveit.logic.sets.enumeration.proper_subset_of_superset
2	reference	59	⊢
3	reference	56	⊢
4	reference	9	⊢
5	reference	22	⊢
6	instantiation	8, 59, 9, 10, 11, 12	⊢
	: , : , :
7	instantiation	13, 14, 15	⊢
	: , : , :
8	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
9	instantiation	34	⊢
	: , : , :
10	instantiation	16, 17	⊢
	: , :
11	instantiation	25, 56, 59, 18	⊢
	: , :
12	instantiation	25, 56, 19, 20	⊢
	: , :
13	axiom		⊢
	proveit.logic.equality.equals_transitivity
14	instantiation	23, 26, 56, 21, 22	⊢
	: , : , : , : , : , : , :
15	instantiation	23, 59, 26, 24	⊢
	: , : , : , : , : , : , :
16	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
17	instantiation	25, 26, 56, 27	⊢
	: , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
19	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
20	instantiation	28, 47, 29, 49, 30, 31^, 32^	⊢
	: , : , :
21	instantiation	33	⊢
	: , :
22	instantiation	33	⊢
	: , :
23	theorem		⊢
	proveit.logic.sets.enumeration.leftward_permutation
24	instantiation	34	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
26	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
27	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
28	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
30	instantiation	35, 36	⊢
	:
31	instantiation	39, 37, 38	⊢
	: , : , :
32	instantiation	39, 40, 41	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
34	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
35	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
37	instantiation	42, 45	⊢
	:
38	instantiation	44, 45, 43	⊢
	: , :
39	theorem		⊢
	proveit.logic.equality.sub_right_side_into
40	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
41	instantiation	44, 45, 46	⊢
	: , :
42	theorem		⊢
	proveit.numbers.addition.elim_zero_right
43	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
44	theorem		⊢
	proveit.numbers.addition.commutation
45	instantiation	57, 48, 47	⊢
	: , : , :
46	instantiation	57, 48, 49	⊢
	: , : , :
47	instantiation	57, 51, 50	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
49	instantiation	57, 51, 52	⊢
	: , : , :
50	instantiation	57, 54, 53	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
52	instantiation	57, 54, 55	⊢
	: , : , :
53	instantiation	57, 58, 56	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
55	instantiation	57, 58, 59	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
57	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
^*equality replacement requirements