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.equality.not_equals_def
2	instantiation	3, 4	⊢
	:
3	axiom		⊢
	proveit.logic.booleans.eq_true_intro
4	instantiation	5, 6	⊢
	: , :
5	theorem		⊢
	proveit.logic.equality.unfold_not_equals
6	instantiation	7, 67, 8	⊢
	: , : , : , : , :
7	theorem		⊢
	proveit.logic.booleans.conjunction.any_from_and
8	instantiation	9, 66, 10, 11	⊢
	: , : , :
9	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_unfold
10	instantiation	23	⊢
	: , : , :
11	instantiation	12, 13, 14	⊢
	: , : , :
12	theorem		⊢
	proveit.logic.equality.sub_left_side_into
13	instantiation	15, 66, 16, 17, 18, 19	⊢
	: , : , :
14	instantiation	20, 21, 22	⊢
	: , : , :
15	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
16	instantiation	23	⊢
	: , : , :
17	instantiation	24, 25	⊢
	: , :
18	instantiation	34, 70, 66, 26	⊢
	: , :
19	instantiation	34, 70, 27, 28	⊢
	: , :
20	axiom		⊢
	proveit.logic.equality.equals_transitivity
21	instantiation	29, 30	⊢
	: , : , :
22	instantiation	31, 67, 32, 33	⊢
	: , : , : , : , : , : , :
23	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
24	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
25	instantiation	34, 67, 70, 35	⊢
	: , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
27	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
28	instantiation	36, 57, 37, 38, 39^, 40^	⊢
	: , : , :
29	axiom		⊢
	proveit.logic.equality.substitution
30	instantiation	45, 41, 42	⊢
	: , : , :
31	theorem		⊢
	proveit.logic.sets.enumeration.leftward_permutation
32	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
33	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
34	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
35	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
36	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
38	instantiation	43, 44	⊢
	:
39	instantiation	45, 46, 47	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
41	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
42	instantiation	51, 48, 49	⊢
	: , :
43	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
44	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
45	theorem		⊢
	proveit.logic.equality.sub_right_side_into
46	instantiation	50, 52	⊢
	:
47	instantiation	51, 52, 53	⊢
	: , :
48	instantiation	68, 56, 54	⊢
	: , : , :
49	instantiation	68, 56, 55	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.addition.elim_zero_right
51	theorem		⊢
	proveit.numbers.addition.commutation
52	instantiation	68, 56, 57	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
54	instantiation	68, 60, 58	⊢
	: , : , :
55	instantiation	68, 60, 59	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
57	instantiation	68, 60, 61	⊢
	: , : , :
58	instantiation	68, 64, 62	⊢
	: , : , :
59	instantiation	68, 64, 63	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
61	instantiation	68, 64, 65	⊢
	: , : , :
62	instantiation	68, 69, 66	⊢
	: , : , :
63	instantiation	68, 69, 67	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
65	instantiation	68, 69, 70	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
68	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements