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	4	⊢
2	instantiation	4, 5, 6	⊢
	: , : , :
3	instantiation	15, 7	⊢
	:
4	axiom		⊢
	proveit.logic.equality.equals_transitivity
5	instantiation	9, 8	⊢
	: , : , :
6	instantiation	9, 10	⊢
	: , : , :
7	instantiation	11, 66, 12, 13	⊢
	: , :
8	instantiation	15, 14	⊢
	:
9	axiom		⊢
	proveit.logic.equality.substitution
10	instantiation	15, 16	⊢
	:
11	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_all
12	instantiation	17	⊢
	: , : , :
13	axiom		⊢
	proveit.logic.booleans.true_axiom
14	instantiation	19, 18	⊢
	: , :
15	axiom		⊢
	proveit.logic.booleans.eq_true_intro
16	instantiation	19, 20	⊢
	: , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
18	instantiation	22, 65, 23, 21	⊢
	: , :
19	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
20	instantiation	22, 66, 23, 24	⊢
	: , :
21	instantiation	29, 53, 30, 25, 26, 27^, 28^	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
23	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
24	instantiation	29, 54, 30, 56, 31, 32^, 33^	⊢
	: , : , :
25	instantiation	67, 59, 34	⊢
	: , : , :
26	instantiation	38, 35	⊢
	:
27	instantiation	42, 36, 37	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
29	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
31	instantiation	38, 39	⊢
	:
32	instantiation	42, 40, 41	⊢
	: , : , :
33	instantiation	42, 43, 44	⊢
	: , : , :
34	instantiation	67, 63, 45	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
36	instantiation	47, 46	⊢
	:
37	instantiation	49, 46, 48	⊢
	: , :
38	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
40	instantiation	47, 50	⊢
	:
41	instantiation	49, 50, 48	⊢
	: , :
42	theorem		⊢
	proveit.logic.equality.sub_right_side_into
43	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_2
44	instantiation	49, 50, 51	⊢
	: , :
45	instantiation	67, 68, 52	⊢
	: , : , :
46	instantiation	67, 55, 53	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.addition.elim_zero_right
48	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
49	theorem		⊢
	proveit.numbers.addition.commutation
50	instantiation	67, 55, 54	⊢
	: , : , :
51	instantiation	67, 55, 56	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
53	instantiation	67, 59, 57	⊢
	: , : , :
54	instantiation	67, 59, 58	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
56	instantiation	67, 59, 60	⊢
	: , : , :
57	instantiation	67, 63, 61	⊢
	: , : , :
58	instantiation	67, 63, 62	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
60	instantiation	67, 63, 64	⊢
	: , : , :
61	instantiation	67, 68, 65	⊢
	: , : , :
62	instantiation	67, 68, 66	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
64	instantiation	67, 68, 69	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
67	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements