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	7, 8, 9	⊢
	: , : , :
4	theorem		⊢
	proveit.logic.equality.sub_left_side_into
5	instantiation	10, 23, 56, 24, 13, 11	⊢
	: , : , : , : , :
6	instantiation	12, 23, 56, 24, 13	⊢
	: , : , : , : , : , : , :
7	axiom		⊢
	proveit.logic.equality.equals_transitivity
8	instantiation	16, 23, 14, 56, 24, 15	⊢
	: , : , : , : , : , : , :
9	instantiation	16, 23, 56, 24, 17	⊢
	: , : , : , : , : , : , :
10	theorem		⊢
	proveit.logic.sets.enumeration.proper_subset_of_superset
11	instantiation	18, 19, 20	⊢
	: , : , :
12	theorem		⊢
	proveit.logic.sets.enumeration.leftward_permutation
13	instantiation	21	⊢
	: , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
15	instantiation	21	⊢
	: , :
16	theorem		⊢
	proveit.logic.sets.enumeration.reduction_right
17	instantiation	21	⊢
	: , :
18	theorem		⊢
	proveit.logic.sets.inclusion.refined_nonmembership
19	instantiation	22, 23, 65, 24, 26	⊢
	: , : , : , :
20	instantiation	25, 65, 26, 27, 28, 29	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
22	theorem		⊢
	proveit.logic.sets.enumeration.subset_eq_of_superset
23	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
24	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
25	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
26	instantiation	30	⊢
	: , : , :
27	instantiation	31, 32	⊢
	: , :
28	instantiation	37, 65, 33, 34	⊢
	: , :
29	instantiation	37, 65, 35, 36	⊢
	: , :
30	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
31	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
32	instantiation	37, 56, 65, 38	⊢
	: , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
34	instantiation	39, 58, 40, 41, 42, 43^, 44^	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
36	theorem		⊢
	proveit.numbers.numerals.decimals.less_3_4
37	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
38	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
39	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
41	instantiation	63, 59, 45	⊢
	: , : , :
42	instantiation	46, 47	⊢
	:
43	instantiation	48, 49, 50	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
45	instantiation	63, 61, 51	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
47	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
48	theorem		⊢
	proveit.logic.equality.sub_right_side_into
49	instantiation	52, 54	⊢
	:
50	instantiation	53, 54, 55	⊢
	: , :
51	instantiation	63, 64, 56	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.addition.elim_zero_right
53	theorem		⊢
	proveit.numbers.addition.commutation
54	instantiation	63, 57, 58	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
56	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
57	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
58	instantiation	63, 59, 60	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
60	instantiation	63, 61, 62	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
62	instantiation	63, 64, 65	⊢
	: , : , :
63	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
64	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
65	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
^*equality replacement requirements