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	theorem		⊢
	proveit.logic.equality.sub_left_side_into
2	instantiation	4, 58, 55, 11, 5, 6	⊢
	: , : , : , : , :
3	instantiation	7, 8, 9	⊢
	: , : , :
4	theorem		⊢
	proveit.logic.sets.enumeration.proper_subset_of_superset
5	instantiation	25	⊢
	: , :
6	instantiation	10, 58, 11, 12, 13, 14	⊢
	: , : , :
7	axiom		⊢
	proveit.logic.equality.equals_transitivity
8	instantiation	16, 27, 58, 15	⊢
	: , : , : , : , : , : , :
9	instantiation	16, 55, 27, 17, 18	⊢
	: , : , : , : , : , : , :
10	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
11	instantiation	24	⊢
	: , : , :
12	instantiation	19, 20	⊢
	: , :
13	instantiation	26, 55, 58, 21	⊢
	: , :
14	instantiation	26, 55, 22, 23	⊢
	: , :
15	instantiation	24	⊢
	: , : , :
16	theorem		⊢
	proveit.logic.sets.enumeration.leftward_permutation
17	instantiation	25	⊢
	: , :
18	instantiation	25	⊢
	: , :
19	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
20	instantiation	26, 27, 55, 28	⊢
	: , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
22	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
23	instantiation	29, 46, 30, 48, 31, 32^, 33^	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
25	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
26	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
27	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
28	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
29	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
31	instantiation	34, 35	⊢
	:
32	instantiation	38, 36, 37	⊢
	: , : , :
33	instantiation	38, 39, 40	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
35	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
36	instantiation	41, 44	⊢
	:
37	instantiation	43, 44, 42	⊢
	: , :
38	theorem		⊢
	proveit.logic.equality.sub_right_side_into
39	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
40	instantiation	43, 44, 45	⊢
	: , :
41	theorem		⊢
	proveit.numbers.addition.elim_zero_right
42	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
43	theorem		⊢
	proveit.numbers.addition.commutation
44	instantiation	56, 47, 46	⊢
	: , : , :
45	instantiation	56, 47, 48	⊢
	: , : , :
46	instantiation	56, 50, 49	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
48	instantiation	56, 50, 51	⊢
	: , : , :
49	instantiation	56, 53, 52	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
51	instantiation	56, 53, 54	⊢
	: , : , :
52	instantiation	56, 57, 55	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
54	instantiation	56, 57, 58	⊢
	: , : , :
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