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	, ⊢
	: , : , : , :
1	reference	13	⊢
2	instantiation	17, 32, 34	⊢
	: , :
3	instantiation	5	⊢
	:
4	instantiation	6, 7	, ⊢
	: , :
5	axiom		⊢
	proveit.logic.equality.equals_reflexivity
6	theorem		⊢
	proveit.logic.equality.equals_reversal
7	instantiation	8, 9, 10	, ⊢
	: , : , :
8	axiom		⊢
	proveit.logic.equality.equals_transitivity
9	instantiation	11, 12	, ⊢
	: , : , :
10	instantiation	13, 14, 15, 16	, ⊢
	: , : , : , :
11	axiom		⊢
	proveit.logic.equality.substitution
12	instantiation	17, 32, 27	, ⊢
	: , :
13	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
14	instantiation	19, 24, 70, 63, 25, 20, 26, 22, 18	, ⊢
	: , : , : , : , : , :
15	instantiation	19, 70, 24, 20, 21, 25, 26, 22, 27, 28	, ⊢
	: , : , : , : , : , :
16	instantiation	23, 63, 24, 25, 26, 27, 28	, ⊢
	: , : , : , : , : , : , : , :
17	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
18	instantiation	68, 39, 29	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.addition.disassociation
20	instantiation	30	⊢
	: , :
21	instantiation	30	⊢
	: , :
22	instantiation	68, 39, 31	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general_rev
24	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
25	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
26	instantiation	33, 32	⊢
	:
27	instantiation	68, 39, 37	⊢
	: , : , :
28	instantiation	33, 34	⊢
	:
29	instantiation	35, 37, 36	⊢
	: , :
30	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
31	instantiation	40, 37	⊢
	:
32	instantiation	68, 39, 38	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.negation.complex_closure
34	instantiation	68, 39, 41	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
36	instantiation	40, 41	⊢
	:
37	instantiation	68, 44, 42	⊢
	: , : , :
38	instantiation	68, 44, 43	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
40	theorem		⊢
	proveit.numbers.negation.real_closure
41	instantiation	68, 44, 45	⊢
	: , : , :
42	instantiation	68, 48, 46	⊢
	: , : , :
43	instantiation	68, 48, 47	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
45	instantiation	68, 48, 59	⊢
	: , : , :
46	instantiation	68, 49, 50	⊢
	: , : , :
47	instantiation	68, 51, 52	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
49	instantiation	56, 53, 62	⊢
	: , :
50	instantiation	54, 55	⊢
	: , :
51	instantiation	56, 59, 57	⊢
	: , :
52	assumption		⊢
53	instantiation	60, 58, 59	⊢
	: , :
54	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
55	assumption		⊢
56	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
57	instantiation	60, 62, 61	⊢
	: , :
58	instantiation	64, 62	⊢
	:
59	instantiation	68, 69, 63	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
61	instantiation	64, 65	⊢
	:
62	instantiation	68, 66, 67	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
64	theorem		⊢
	proveit.numbers.negation.int_closure
65	instantiation	68, 69, 70	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
67	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
68	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat2