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.membership_unfolding
2	instantiation	3, 4, 5	⊢
	: , : , :
3	theorem		⊢
	proveit.logic.sets.subtraction.membership_folding
4	instantiation	6, 44, 20, 7	⊢
	: , : , : , : , :
5	instantiation	26, 8, 9	⊢
	: , : , :
6	theorem		⊢
	proveit.logic.sets.enumeration.in_enumerated_set
7	instantiation	10	⊢
	: , : , :
8	instantiation	11, 41, 12, 13, 14	⊢
	: , : , :
9	instantiation	15, 16	⊢
	: , :
10	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
11	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
12	instantiation	17	⊢
	: , :
13	instantiation	18, 19	⊢
	: , :
14	instantiation	24, 41, 20, 21	⊢
	: , :
15	theorem		⊢
	proveit.logic.equality.equals_reversal
16	instantiation	22, 23	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
18	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
19	instantiation	24, 44, 41, 25	⊢
	: , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
21	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
22	axiom		⊢
	proveit.logic.equality.substitution
23	instantiation	26, 27, 28	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
25	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
26	theorem		⊢
	proveit.logic.equality.sub_right_side_into
27	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
28	instantiation	29, 30, 31	⊢
	: , :
29	theorem		⊢
	proveit.numbers.addition.commutation
30	instantiation	42, 33, 32	⊢
	: , : , :
31	instantiation	42, 33, 34	⊢
	: , : , :
32	instantiation	42, 36, 35	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
34	instantiation	42, 36, 37	⊢
	: , : , :
35	instantiation	42, 39, 38	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
37	instantiation	42, 39, 40	⊢
	: , : , :
38	instantiation	42, 43, 41	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
40	instantiation	42, 43, 44	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
42	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
43	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat1