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	⊢
	:
1	axiom		⊢
	proveit.logic.booleans.eq_true_intro
2	instantiation	3, 4	⊢
	: , :
3	theorem		⊢
	proveit.logic.equality.unfold_not_equals
4	instantiation	5, 65, 6	⊢
	: , : , : , : , :
5	theorem		⊢
	proveit.logic.booleans.conjunction.any_from_and
6	instantiation	7, 64, 8, 9	⊢
	: , : , :
7	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_unfold
8	instantiation	21	⊢
	: , : , :
9	instantiation	10, 11, 12	⊢
	: , : , :
10	theorem		⊢
	proveit.logic.equality.sub_left_side_into
11	instantiation	13, 64, 14, 15, 16, 17	⊢
	: , : , :
12	instantiation	18, 19, 20	⊢
	: , : , :
13	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
14	instantiation	21	⊢
	: , : , :
15	instantiation	22, 23	⊢
	: , :
16	instantiation	32, 68, 64, 24	⊢
	: , :
17	instantiation	32, 68, 25, 26	⊢
	: , :
18	axiom		⊢
	proveit.logic.equality.equals_transitivity
19	instantiation	27, 28	⊢
	: , : , :
20	instantiation	29, 65, 30, 31	⊢
	: , : , : , : , : , : , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
22	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
23	instantiation	32, 65, 68, 33	⊢
	: , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
25	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
26	instantiation	34, 55, 35, 36, 37^, 38^	⊢
	: , : , :
27	axiom		⊢
	proveit.logic.equality.substitution
28	instantiation	43, 39, 40	⊢
	: , : , :
29	theorem		⊢
	proveit.logic.sets.enumeration.leftward_permutation
30	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
31	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
32	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
33	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
34	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
36	instantiation	41, 42	⊢
	:
37	instantiation	43, 44, 45	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
39	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
40	instantiation	49, 46, 47	⊢
	: , :
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	48, 50	⊢
	:
45	instantiation	49, 50, 51	⊢
	: , :
46	instantiation	66, 54, 52	⊢
	: , : , :
47	instantiation	66, 54, 53	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.addition.elim_zero_right
49	theorem		⊢
	proveit.numbers.addition.commutation
50	instantiation	66, 54, 55	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
52	instantiation	66, 58, 56	⊢
	: , : , :
53	instantiation	66, 58, 57	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
55	instantiation	66, 58, 59	⊢
	: , : , :
56	instantiation	66, 62, 60	⊢
	: , : , :
57	instantiation	66, 62, 61	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
59	instantiation	66, 62, 63	⊢
	: , : , :
60	instantiation	66, 67, 64	⊢
	: , : , :
61	instantiation	66, 67, 65	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
63	instantiation	66, 67, 68	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
65	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
66	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
67	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements