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^, 6^, 7^*	⊢
	: , : , : , : , :
1	theorem		⊢
	proveit.numbers.summation.index_shift
2	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
3	instantiation	53, 54, 8	⊢
	: , : , :
4	reference	49	⊢
5	instantiation	9, 35	⊢
	:
6	theorem		⊢
	proveit.numbers.numerals.decimals.add_9_2
7	instantiation	10, 11, 12	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.numerals.decimals.nat9
9	theorem		⊢
	proveit.numbers.addition.elim_zero_left
10	axiom		⊢
	proveit.logic.equality.equals_transitivity
11	instantiation	13, 16, 55, 62, 18, 14, 19, 31, 30	⊢
	: , : , : , : , : , :
12	instantiation	15, 62, 55, 16, 17, 18, 19, 31, 30, 20^*	⊢
	: , : , : , : , : , :
13	theorem		⊢
	proveit.numbers.addition.disassociation
14	instantiation	21	⊢
	: , :
15	theorem		⊢
	proveit.numbers.addition.association
16	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
17	instantiation	21	⊢
	: , :
18	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
19	instantiation	53, 39, 22	⊢
	: , : , :
20	instantiation	23, 24, 25	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
22	instantiation	53, 44, 26	⊢
	: , : , :
23	theorem		⊢
	proveit.logic.equality.sub_right_side_into
24	instantiation	27, 30, 35, 28	⊢
	: , : , :
25	instantiation	29, 30, 31	⊢
	: , :
26	instantiation	53, 48, 32	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
28	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
29	theorem		⊢
	proveit.numbers.addition.commutation
30	instantiation	53, 39, 33	⊢
	: , : , :
31	instantiation	34, 35	⊢
	:
32	instantiation	53, 36, 37	⊢
	: , : , :
33	instantiation	53, 44, 38	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.negation.complex_closure
35	instantiation	53, 39, 40	⊢
	: , : , :
36	instantiation	41, 49, 42	⊢
	: , :
37	assumption		⊢
38	instantiation	53, 48, 43	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
40	instantiation	53, 44, 45	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
42	instantiation	53, 46, 47	⊢
	: , : , :
43	instantiation	53, 54, 62	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
45	instantiation	53, 48, 49	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
47	instantiation	50, 62, 51, 52	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
49	instantiation	53, 54, 55	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.deci_sequence_is_nat_pos
51	instantiation	56, 62, 57	⊢
	:
52	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
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.nat2
56	theorem		⊢
	proveit.numbers.numerals.decimals.n_in_digits
57	instantiation	58, 59, 60	⊢
	: , :
58	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
59	instantiation	61, 62	⊢
	:
60	instantiation	63, 64	⊢
	:
61	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
63	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
64	theorem		⊢
	proveit.numbers.numerals.decimals.posnat9
^*equality replacement requirements