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.conjunction.any_from_and
2	reference	62	⊢
3	instantiation	4, 61, 5, 6	⊢
	: , : , :
4	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_unfold
5	instantiation	18	⊢
	: , : , :
6	instantiation	7, 8, 9	⊢
	: , : , :
7	theorem		⊢
	proveit.logic.equality.sub_left_side_into
8	instantiation	10, 61, 11, 12, 13, 14	⊢
	: , : , :
9	instantiation	15, 16, 17	⊢
	: , : , :
10	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
11	instantiation	18	⊢
	: , : , :
12	instantiation	19, 20	⊢
	: , :
13	instantiation	29, 65, 61, 21	⊢
	: , :
14	instantiation	29, 65, 22, 23	⊢
	: , :
15	axiom		⊢
	proveit.logic.equality.equals_transitivity
16	instantiation	24, 25	⊢
	: , : , :
17	instantiation	26, 62, 27, 28	⊢
	: , : , : , : , : , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
19	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
20	instantiation	29, 62, 65, 30	⊢
	: , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
22	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
23	instantiation	31, 52, 32, 33, 34^, 35^	⊢
	: , : , :
24	axiom		⊢
	proveit.logic.equality.substitution
25	instantiation	40, 36, 37	⊢
	: , : , :
26	theorem		⊢
	proveit.logic.sets.enumeration.leftward_permutation
27	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
28	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
29	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
30	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
31	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
33	instantiation	38, 39	⊢
	:
34	instantiation	40, 41, 42	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
36	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
37	instantiation	46, 43, 44	⊢
	: , :
38	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
40	theorem		⊢
	proveit.logic.equality.sub_right_side_into
41	instantiation	45, 47	⊢
	:
42	instantiation	46, 47, 48	⊢
	: , :
43	instantiation	63, 51, 49	⊢
	: , : , :
44	instantiation	63, 51, 50	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.addition.elim_zero_right
46	theorem		⊢
	proveit.numbers.addition.commutation
47	instantiation	63, 51, 52	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
49	instantiation	63, 55, 53	⊢
	: , : , :
50	instantiation	63, 55, 54	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
52	instantiation	63, 55, 56	⊢
	: , : , :
53	instantiation	63, 59, 57	⊢
	: , : , :
54	instantiation	63, 59, 58	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
56	instantiation	63, 59, 60	⊢
	: , : , :
57	instantiation	63, 64, 61	⊢
	: , : , :
58	instantiation	63, 64, 62	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
60	instantiation	63, 64, 65	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
63	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
64	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
65	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements