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	⊢
	: , : , :
1	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_unfold
2	reference	59	⊢
3	instantiation	16	⊢
	: , : , :
4	instantiation	5, 6, 7	⊢
	: , : , :
5	theorem		⊢
	proveit.logic.equality.sub_left_side_into
6	instantiation	8, 59, 9, 10, 11, 12	⊢
	: , : , :
7	instantiation	13, 14, 15	⊢
	: , : , :
8	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
9	instantiation	16	⊢
	: , : , :
10	instantiation	17, 18	⊢
	: , :
11	instantiation	27, 63, 59, 19	⊢
	: , :
12	instantiation	27, 63, 20, 21	⊢
	: , :
13	axiom		⊢
	proveit.logic.equality.equals_transitivity
14	instantiation	22, 23	⊢
	: , : , :
15	instantiation	24, 60, 25, 26	⊢
	: , : , : , : , : , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
17	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
18	instantiation	27, 60, 63, 28	⊢
	: , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
20	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
21	instantiation	29, 50, 30, 31, 32^, 33^	⊢
	: , : , :
22	axiom		⊢
	proveit.logic.equality.substitution
23	instantiation	38, 34, 35	⊢
	: , : , :
24	theorem		⊢
	proveit.logic.sets.enumeration.leftward_permutation
25	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
26	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
27	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
28	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
29	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
31	instantiation	36, 37	⊢
	:
32	instantiation	38, 39, 40	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
34	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
35	instantiation	44, 41, 42	⊢
	: , :
36	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
37	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
38	theorem		⊢
	proveit.logic.equality.sub_right_side_into
39	instantiation	43, 45	⊢
	:
40	instantiation	44, 45, 46	⊢
	: , :
41	instantiation	61, 49, 47	⊢
	: , : , :
42	instantiation	61, 49, 48	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.addition.elim_zero_right
44	theorem		⊢
	proveit.numbers.addition.commutation
45	instantiation	61, 49, 50	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
47	instantiation	61, 53, 51	⊢
	: , : , :
48	instantiation	61, 53, 52	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
50	instantiation	61, 53, 54	⊢
	: , : , :
51	instantiation	61, 57, 55	⊢
	: , : , :
52	instantiation	61, 57, 56	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
54	instantiation	61, 57, 58	⊢
	: , : , :
55	instantiation	61, 62, 59	⊢
	: , : , :
56	instantiation	61, 62, 60	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
58	instantiation	61, 62, 63	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
60	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
61	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
62	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements