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