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, 13, 46, 14, 7, 5	⊢
	: , : , : , : , :
3	instantiation	6, 13, 46, 14, 7	⊢
	: , : , : , : , : , : , :
4	theorem		⊢
	proveit.logic.sets.enumeration.proper_subset_of_superset
5	instantiation	8, 9, 10	⊢
	: , : , :
6	theorem		⊢
	proveit.logic.sets.enumeration.leftward_permutation
7	instantiation	11	⊢
	: , :
8	theorem		⊢
	proveit.logic.sets.inclusion.refined_nonmembership
9	instantiation	12, 13, 55, 14, 16	⊢
	: , : , : , :
10	instantiation	15, 55, 16, 17, 18, 19	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
12	theorem		⊢
	proveit.logic.sets.enumeration.subset_eq_of_superset
13	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
14	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
15	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
16	instantiation	20	⊢
	: , : , :
17	instantiation	21, 22	⊢
	: , :
18	instantiation	27, 55, 23, 24	⊢
	: , :
19	instantiation	27, 55, 25, 26	⊢
	: , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
21	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
22	instantiation	27, 46, 55, 28	⊢
	: , :
23	theorem		⊢
	proveit.numbers.numerals.decimals.nat5
24	instantiation	29, 48, 30, 31, 32, 33^, 34^	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
26	theorem		⊢
	proveit.numbers.numerals.decimals.less_3_4
27	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
28	theorem		⊢
	proveit.numbers.numerals.decimals.less_2_3
29	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
31	instantiation	53, 49, 35	⊢
	: , : , :
32	instantiation	36, 37	⊢
	:
33	instantiation	38, 39, 40	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_3
35	instantiation	53, 51, 41	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
37	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
38	theorem		⊢
	proveit.logic.equality.sub_right_side_into
39	instantiation	42, 44	⊢
	:
40	instantiation	43, 44, 45	⊢
	: , :
41	instantiation	53, 54, 46	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.addition.elim_zero_right
43	theorem		⊢
	proveit.numbers.addition.commutation
44	instantiation	53, 47, 48	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
47	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
48	instantiation	53, 49, 50	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
50	instantiation	53, 51, 52	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
52	instantiation	53, 54, 55	⊢
	: , : , :
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