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, 4, 5	⊢
	: , : , :
1	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
2	reference	43	⊢
3	instantiation	6	⊢
	: , :
4	instantiation	8, 7	⊢
	: , :
5	instantiation	8, 9	⊢
	: , :
6	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
7	instantiation	11, 52, 12, 10	⊢
	: , :
8	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
9	instantiation	11, 55, 12, 13	⊢
	: , :
10	instantiation	18, 42, 19, 14, 15, 16^, 17^	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
12	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
13	instantiation	18, 45, 19, 20, 21, 22^, 23^	⊢
	: , : , :
14	instantiation	53, 47, 24	⊢
	: , : , :
15	instantiation	29, 25	⊢
	:
16	instantiation	31, 26, 27	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
18	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
19	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
20	instantiation	53, 47, 28	⊢
	: , : , :
21	instantiation	29, 30	⊢
	:
22	instantiation	31, 32, 33	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
24	instantiation	53, 50, 34	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
26	instantiation	37, 35	⊢
	:
27	instantiation	38, 35, 40	⊢
	: , :
28	instantiation	53, 50, 36	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
30	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
31	theorem		⊢
	proveit.logic.equality.sub_right_side_into
32	instantiation	37, 39	⊢
	:
33	instantiation	38, 39, 40	⊢
	: , :
34	instantiation	53, 54, 41	⊢
	: , : , :
35	instantiation	53, 44, 42	⊢
	: , : , :
36	instantiation	53, 54, 43	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.addition.elim_zero_right
38	theorem		⊢
	proveit.numbers.addition.commutation
39	instantiation	53, 44, 45	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
42	instantiation	53, 47, 46	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
45	instantiation	53, 47, 48	⊢
	: , : , :
46	instantiation	53, 50, 49	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
48	instantiation	53, 50, 51	⊢
	: , : , :
49	instantiation	53, 54, 52	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
51	instantiation	53, 54, 55	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
53	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
^*equality replacement requirements