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	theorem		⊢
	proveit.logic.equality.sub_left_side_into
2	instantiation	4, 63, 11, 8, 5	⊢
	: , : , : , : , :
3	instantiation	6, 63, 7, 11, 8, 9	⊢
	: , : , : , : , : , : , :
4	theorem		⊢
	proveit.logic.sets.enumeration.proper_subset_of_superset
5	instantiation	10, 63, 11, 12, 13	⊢
	: , : , :
6	theorem		⊢
	proveit.logic.sets.enumeration.leftward_permutation
7	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
8	instantiation	14	⊢
	: , :
9	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
10	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
11	instantiation	14	⊢
	: , :
12	instantiation	16, 15	⊢
	: , :
13	instantiation	16, 17	⊢
	: , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
15	instantiation	19, 62, 20, 18	⊢
	: , :
16	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
17	instantiation	19, 63, 20, 21	⊢
	: , :
18	instantiation	26, 50, 27, 22, 23, 24^, 25^	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
20	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
21	instantiation	26, 51, 27, 53, 28, 29^, 30^	⊢
	: , : , :
22	instantiation	64, 56, 31	⊢
	: , : , :
23	instantiation	35, 32	⊢
	:
24	instantiation	39, 33, 34	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
26	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
28	instantiation	35, 36	⊢
	:
29	instantiation	39, 37, 38	⊢
	: , : , :
30	instantiation	39, 40, 41	⊢
	: , : , :
31	instantiation	64, 60, 42	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
33	instantiation	44, 43	⊢
	:
34	instantiation	46, 43, 45	⊢
	: , :
35	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
37	instantiation	44, 47	⊢
	:
38	instantiation	46, 47, 45	⊢
	: , :
39	theorem		⊢
	proveit.logic.equality.sub_right_side_into
40	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
41	instantiation	46, 47, 48	⊢
	: , :
42	instantiation	64, 65, 49	⊢
	: , : , :
43	instantiation	64, 52, 50	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.addition.elim_zero_right
45	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
46	theorem		⊢
	proveit.numbers.addition.commutation
47	instantiation	64, 52, 51	⊢
	: , : , :
48	instantiation	64, 52, 53	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
50	instantiation	64, 56, 54	⊢
	: , : , :
51	instantiation	64, 56, 55	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
53	instantiation	64, 56, 57	⊢
	: , : , :
54	instantiation	64, 60, 58	⊢
	: , : , :
55	instantiation	64, 60, 59	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
57	instantiation	64, 60, 61	⊢
	: , : , :
58	instantiation	64, 65, 62	⊢
	: , : , :
59	instantiation	64, 65, 63	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
61	instantiation	64, 65, 66	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
64	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
65	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
^*equality replacement requirements