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, 55, 5, 6, 7, 8	⊢
	: , : , :
3	instantiation	9, 10, 11	⊢
	: , : , :
4	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
5	instantiation	12	⊢
	: , : , :
6	instantiation	13, 14	⊢
	: , :
7	instantiation	23, 59, 55, 15	⊢
	: , :
8	instantiation	23, 59, 16, 17	⊢
	: , :
9	axiom		⊢
	proveit.logic.equality.equals_transitivity
10	instantiation	18, 19	⊢
	: , : , :
11	instantiation	20, 56, 21, 22	⊢
	: , : , : , : , : , : , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
13	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
14	instantiation	23, 56, 59, 24	⊢
	: , :
15	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
16	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
17	instantiation	25, 46, 26, 27, 28^, 29^	⊢
	: , : , :
18	axiom		⊢
	proveit.logic.equality.substitution
19	instantiation	34, 30, 31	⊢
	: , : , :
20	theorem		⊢
	proveit.logic.sets.enumeration.leftward_permutation
21	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
22	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
23	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
24	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
25	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
27	instantiation	32, 33	⊢
	:
28	instantiation	34, 35, 36	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
30	theorem		⊢
	proveit.numbers.numerals.decimals.add_3_1
31	instantiation	40, 37, 38	⊢
	: , :
32	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
33	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
34	theorem		⊢
	proveit.logic.equality.sub_right_side_into
35	instantiation	39, 41	⊢
	:
36	instantiation	40, 41, 42	⊢
	: , :
37	instantiation	57, 45, 43	⊢
	: , : , :
38	instantiation	57, 45, 44	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.addition.elim_zero_right
40	theorem		⊢
	proveit.numbers.addition.commutation
41	instantiation	57, 45, 46	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
43	instantiation	57, 49, 47	⊢
	: , : , :
44	instantiation	57, 49, 48	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
46	instantiation	57, 49, 50	⊢
	: , : , :
47	instantiation	57, 53, 51	⊢
	: , : , :
48	instantiation	57, 53, 52	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
50	instantiation	57, 53, 54	⊢
	: , : , :
51	instantiation	57, 58, 55	⊢
	: , : , :
52	instantiation	57, 58, 56	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
54	instantiation	57, 58, 59	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
56	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
57	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements