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	⊢
	: , : , :
1	theorem		⊢
	proveit.logic.sets.subtraction.nonmembership_unfolding
2	instantiation	22, 3, 4	⊢
	: , : , :
3	instantiation	5, 6	⊢
	: , : , :
4	instantiation	17, 7	⊢
	: , : , :
5	theorem		⊢
	proveit.logic.sets.subtraction.nonmembership_folding
6	instantiation	8, 9, 10	⊢
	: , :
7	instantiation	11, 12	⊢
	: , :
8	theorem		⊢
	proveit.logic.booleans.disjunction.or_if_only_right
9	instantiation	13, 14	⊢
	: , :
10	instantiation	19, 41, 15, 16	⊢
	: , : , : , : , :
11	theorem		⊢
	proveit.logic.equality.equals_reversal
12	instantiation	17, 18	⊢
	: , : , :
13	theorem		⊢
	proveit.logic.sets.membership.double_negated_membership
14	instantiation	19, 38, 20, 21	⊢
	: , : , : , : , :
15	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
16	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
17	axiom		⊢
	proveit.logic.equality.substitution
18	instantiation	22, 23, 24	⊢
	: , : , :
19	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
20	instantiation	25	⊢
	: , :
21	instantiation	25	⊢
	: , :
22	theorem		⊢
	proveit.logic.equality.sub_right_side_into
23	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
24	instantiation	26, 27, 28	⊢
	: , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
26	theorem		⊢
	proveit.numbers.addition.commutation
27	instantiation	39, 30, 29	⊢
	: , : , :
28	instantiation	39, 30, 31	⊢
	: , : , :
29	instantiation	39, 33, 32	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
31	instantiation	39, 33, 34	⊢
	: , : , :
32	instantiation	39, 36, 35	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
34	instantiation	39, 36, 37	⊢
	: , : , :
35	instantiation	39, 40, 38	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
37	instantiation	39, 40, 41	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
39	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
40	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat1