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	55	⊢
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, 54, 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, 43, 19, 45, 20, 21^, 22^	⊢
	: , : , :
14	instantiation	56, 48, 23	⊢
	: , : , :
15	instantiation	27, 24	⊢
	:
16	instantiation	31, 25, 26	⊢
	: , : , :
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	27, 28	⊢
	:
21	instantiation	31, 29, 30	⊢
	: , : , :
22	instantiation	31, 32, 33	⊢
	: , : , :
23	instantiation	56, 52, 34	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
25	instantiation	36, 35	⊢
	:
26	instantiation	38, 35, 37	⊢
	: , :
27	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
28	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
29	instantiation	36, 39	⊢
	:
30	instantiation	38, 39, 37	⊢
	: , :
31	theorem		⊢
	proveit.logic.equality.sub_right_side_into
32	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
33	instantiation	38, 39, 40	⊢
	: , :
34	instantiation	56, 57, 41	⊢
	: , : , :
35	instantiation	56, 44, 42	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.addition.elim_zero_right
37	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
38	theorem		⊢
	proveit.numbers.addition.commutation
39	instantiation	56, 44, 43	⊢
	: , : , :
40	instantiation	56, 44, 45	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
42	instantiation	56, 48, 46	⊢
	: , : , :
43	instantiation	56, 48, 47	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
45	instantiation	56, 48, 49	⊢
	: , : , :
46	instantiation	56, 52, 50	⊢
	: , : , :
47	instantiation	56, 52, 51	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
49	instantiation	56, 52, 53	⊢
	: , : , :
50	instantiation	56, 57, 54	⊢
	: , : , :
51	instantiation	56, 57, 55	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
53	instantiation	56, 57, 58	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
56	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
57	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
58	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
^*equality replacement requirements