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	reference	43	⊢
3	instantiation	51, 52, 8	⊢
	: , : , :
4	reference	50	⊢
5	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
6	theorem		⊢
	proveit.numbers.numerals.decimals.add_6_1
7	instantiation	9, 10, 11	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.numerals.decimals.nat6
9	axiom		⊢
	proveit.logic.equality.equals_transitivity
10	instantiation	12, 15, 48, 53, 17, 13, 18, 30, 29	⊢
	: , : , : , : , : , :
11	instantiation	14, 53, 48, 15, 16, 17, 18, 30, 29, 19^*	⊢
	: , : , : , : , : , :
12	theorem		⊢
	proveit.numbers.addition.disassociation
13	instantiation	20	⊢
	: , :
14	theorem		⊢
	proveit.numbers.addition.association
15	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
16	instantiation	20	⊢
	: , :
17	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
18	instantiation	51, 38, 21	⊢
	: , : , :
19	instantiation	22, 23, 24	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
21	instantiation	51, 44, 25	⊢
	: , : , :
22	theorem		⊢
	proveit.logic.equality.sub_right_side_into
23	instantiation	26, 34, 29, 27	⊢
	: , : , :
24	instantiation	28, 29, 30	⊢
	: , :
25	instantiation	51, 49, 31	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
27	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
28	theorem		⊢
	proveit.numbers.addition.commutation
29	instantiation	51, 38, 32	⊢
	: , : , :
30	instantiation	33, 34	⊢
	:
31	instantiation	51, 35, 36	⊢
	: , : , :
32	instantiation	51, 44, 37	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.negation.complex_closure
34	instantiation	51, 38, 39	⊢
	: , : , :
35	instantiation	40, 41, 42	⊢
	: , :
36	assumption		⊢
37	instantiation	51, 49, 43	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
39	instantiation	51, 44, 45	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
41	instantiation	51, 52, 46	⊢
	: , : , :
42	instantiation	51, 52, 47	⊢
	: , : , :
43	instantiation	51, 52, 48	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
45	instantiation	51, 49, 50	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat7
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
49	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
50	instantiation	51, 52, 53	⊢
	: , : , :
51	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
52	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements