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	reference	11	⊢
2	instantiation	27, 4	⊢
	: , : , :
3	instantiation	11, 5, 6	⊢
	: , : , :
4	instantiation	11, 7, 8	⊢
	: , : , :
5	instantiation	9, 61, 10	⊢
	: , : , :
6	instantiation	11, 12, 13	⊢
	: , : , :
7	instantiation	27, 14	⊢
	: , : , :
8	instantiation	15, 62, 16, 17	⊢
	: , : , : , : , : , : , :
9	axiom		⊢
	proveit.logic.sets.enumeration.enum_set_def
10	instantiation	38	⊢
	: , : , :
11	axiom		⊢
	proveit.logic.equality.equals_transitivity
12	instantiation	18, 19, 20, 21	⊢
	: , : , : , :
13	instantiation	36, 22	⊢
	:
14	instantiation	65, 23, 24	⊢
	: , : , :
15	theorem		⊢
	proveit.logic.sets.enumeration.leftward_permutation
16	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
17	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
18	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
19	instantiation	27, 25	⊢
	: , : , :
20	instantiation	27, 26	⊢
	: , : , :
21	instantiation	27, 28	⊢
	: , : , :
22	instantiation	29, 61, 30, 31	⊢
	: , :
23	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
24	instantiation	69, 32, 33	⊢
	: , :
25	instantiation	36, 34	⊢
	:
26	instantiation	36, 35	⊢
	:
27	axiom		⊢
	proveit.logic.equality.substitution
28	instantiation	36, 37	⊢
	:
29	theorem		⊢
	proveit.logic.booleans.disjunction.not_or_if_not_any
30	instantiation	38	⊢
	: , : , :
31	theorem		⊢
	proveit.logic.booleans.negation.not_false
32	instantiation	78, 72, 39	⊢
	: , : , :
33	instantiation	78, 72, 40	⊢
	: , : , :
34	instantiation	43, 41	⊢
	: , :
35	instantiation	43, 42	⊢
	: , :
36	axiom		⊢
	proveit.logic.booleans.negation.negation_elim
37	instantiation	43, 44	⊢
	: , :
38	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
39	instantiation	78, 74, 45	⊢
	: , : , :
40	instantiation	78, 74, 46	⊢
	: , : , :
41	instantiation	47, 48	⊢
	: , :
42	instantiation	54, 80, 61, 49	⊢
	: , :
43	theorem		⊢
	proveit.logic.equality.unfold_not_equals
44	instantiation	54, 80, 50, 51	⊢
	: , :
45	instantiation	78, 76, 52	⊢
	: , : , :
46	instantiation	78, 76, 53	⊢
	: , : , :
47	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
48	instantiation	54, 62, 80, 55	⊢
	: , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
51	instantiation	56, 73, 57, 58, 59^, 60^	⊢
	: , : , :
52	instantiation	78, 79, 61	⊢
	: , : , :
53	instantiation	78, 79, 62	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
55	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
56	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
58	instantiation	63, 64	⊢
	:
59	instantiation	65, 66, 67	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
63	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
64	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
65	theorem		⊢
	proveit.logic.equality.sub_right_side_into
66	instantiation	68, 70	⊢
	:
67	instantiation	69, 70, 71	⊢
	: , :
68	theorem		⊢
	proveit.numbers.addition.elim_zero_right
69	theorem		⊢
	proveit.numbers.addition.commutation
70	instantiation	78, 72, 73	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
72	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
73	instantiation	78, 74, 75	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
75	instantiation	78, 76, 77	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
77	instantiation	78, 79, 80	⊢
	: , : , :
78	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
79	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements