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	reference	4	⊢
2	instantiation	4, 5, 6	⊢
	: , : , :
3	instantiation	17, 55, 18, 19	⊢
	: , : , : , : , : , : , :
4	theorem		⊢
	proveit.logic.equality.sub_left_side_into
5	instantiation	7, 46, 18, 13, 19, 8	⊢
	: , : , : , : , :
6	instantiation	9, 10, 11	⊢
	: , : , :
7	theorem		⊢
	proveit.logic.sets.enumeration.proper_subset_of_superset
8	instantiation	12, 46, 13, 14, 15	⊢
	: , : , :
9	axiom		⊢
	proveit.logic.equality.equals_transitivity
10	instantiation	17, 18, 55, 46, 19, 16	⊢
	: , : , : , : , : , : , :
11	instantiation	17, 18, 46, 19, 20	⊢
	: , : , : , : , : , : , :
12	theorem		⊢
	proveit.logic.sets.enumeration.nonmembership_fold
13	instantiation	24	⊢
	: , :
14	instantiation	22, 21	⊢
	: , :
15	instantiation	22, 23	⊢
	: , :
16	instantiation	24	⊢
	: , :
17	theorem		⊢
	proveit.logic.sets.enumeration.reduction_right
18	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
19	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
20	instantiation	24	⊢
	: , :
21	instantiation	26, 55, 27, 25	⊢
	: , :
22	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
23	instantiation	26, 46, 27, 28	⊢
	: , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
25	instantiation	29, 48, 30, 31, 32, 33^, 34^	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq_nat
27	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
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_1
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.nat1
^*equality replacement requirements