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, 5, 6, 7	⊢
	: , : , : , :
1	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
2	reference	63	⊢
3	instantiation	8	⊢
	: , : , :
4	instantiation	8	⊢
	: , : , :
5	instantiation	11, 9^*	⊢
	: , :
6	instantiation	11, 10^*	⊢
	: , :
7	instantiation	11, 12^*	⊢
	: , :
8	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
9	instantiation	15, 13, 17	⊢
	: , : , :
10	instantiation	15, 14, 17	⊢
	: , : , :
11	axiom		⊢
	proveit.logic.equality.not_equals_def
12	instantiation	15, 16, 17	⊢
	: , : , :
13	instantiation	20, 18	⊢
	: , : , :
14	instantiation	20, 19	⊢
	: , : , :
15	axiom		⊢
	proveit.logic.equality.equals_transitivity
16	instantiation	20, 21	⊢
	: , : , :
17	axiom		⊢
	proveit.logic.booleans.negation.not_f
18	instantiation	24, 22	⊢
	:
19	instantiation	24, 23	⊢
	:
20	axiom		⊢
	proveit.logic.equality.substitution
21	instantiation	24, 25	⊢
	:
22	instantiation	28, 26	⊢
	: , :
23	instantiation	28, 27	⊢
	: , :
24	axiom		⊢
	proveit.logic.booleans.negation.negation_elim
25	instantiation	28, 29	⊢
	: , :
26	instantiation	32, 30	⊢
	: , :
27	instantiation	32, 31	⊢
	: , :
28	theorem		⊢
	proveit.logic.equality.unfold_not_equals
29	instantiation	32, 33	⊢
	: , :
30	instantiation	36, 73, 37, 34	⊢
	: , :
31	instantiation	36, 76, 37, 35	⊢
	: , :
32	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
33	instantiation	36, 63, 37, 38	⊢
	: , :
34	instantiation	43, 64, 44, 39, 40, 41^, 42^	⊢
	: , : , :
35	instantiation	43, 66, 44, 45, 46^, 47^	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
37	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
38	theorem		⊢
	proveit.numbers.numerals.decimals.less_3_4
39	instantiation	74, 68, 48	⊢
	: , : , :
40	instantiation	52, 49	⊢
	:
41	instantiation	54, 50, 51	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
43	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
45	instantiation	52, 53	⊢
	:
46	instantiation	54, 55, 56	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
48	instantiation	74, 71, 57	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
50	instantiation	59, 58	⊢
	:
51	instantiation	60, 58, 62	⊢
	: , :
52	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
53	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
54	theorem		⊢
	proveit.logic.equality.sub_right_side_into
55	instantiation	59, 61	⊢
	:
56	instantiation	60, 61, 62	⊢
	: , :
57	instantiation	74, 75, 63	⊢
	: , : , :
58	instantiation	74, 65, 64	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.addition.elim_zero_right
60	theorem		⊢
	proveit.numbers.addition.commutation
61	instantiation	74, 65, 66	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
64	instantiation	74, 68, 67	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
66	instantiation	74, 68, 69	⊢
	: , : , :
67	instantiation	74, 71, 70	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
69	instantiation	74, 71, 72	⊢
	: , : , :
70	instantiation	74, 75, 73	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
72	instantiation	74, 75, 76	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
74	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
75	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
76	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements