# 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 typerequirementsstatement
0instantiation1, 2, 3,  ⊢
: , : , :
1reference15
2instantiation13, 4
: , : , :
3instantiation15, 5, 6,  ⊢
: , : , :
4instantiation15, 7, 8
: , : , :
5instantiation20, 58, 68, 21, 9, 22, 27, 34, 11,  ⊢
: , : , : , : , : , :
6instantiation10, 34, 11, 12,  ⊢
: , : , :
7instantiation13, 14
: , : , :
8instantiation15, 16, 17
: , : , :
9instantiation30
: , :
10theorem
11instantiation33, 18,  ⊢
:
12instantiation35
:
13axiom
proveit.logic.equality.substitution
14instantiation19, 34, 26
: , :
15axiom
proveit.logic.equality.equals_transitivity
16instantiation20, 21, 68, 58, 22, 23, 27, 24, 26
: , : , : , : , : , :
17instantiation25, 26, 27, 28
: , : , :
18instantiation66, 39, 29,  ⊢
: , : , :
19theorem
proveit.numbers.negation.distribute_neg_through_binary_sum
20theorem
21axiom
proveit.numbers.number_sets.natural_numbers.zero_in_nats
22theorem
proveit.core_expr_types.tuples.tuple_len_0_typical_eq
23instantiation30
: , :
24instantiation66, 39, 31
: , : , :
25theorem
26instantiation66, 39, 32
: , : , :
27instantiation33, 34
:
28instantiation35
:
29instantiation66, 43, 36,  ⊢
: , : , :
30theorem
proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
31instantiation66, 43, 37
: , : , :
32instantiation66, 43, 38
: , : , :
33theorem
proveit.numbers.negation.complex_closure
34instantiation66, 39, 40
: , : , :
35axiom
proveit.logic.equality.equals_reflexivity
36instantiation66, 47, 41,  ⊢
: , : , :
37instantiation66, 47, 42
: , : , :
38instantiation66, 47, 56
: , : , :
39theorem
proveit.numbers.number_sets.complex_numbers.real_within_complex
40instantiation66, 43, 44
: , : , :
41instantiation66, 45, 46,  ⊢
: , : , :
42instantiation64, 56
:
43theorem
proveit.numbers.number_sets.real_numbers.rational_within_real
44instantiation66, 47, 52
: , : , :
45instantiation55, 48, 49
: , :
46assumption
47theorem
proveit.numbers.number_sets.rational_numbers.int_within_rational
48instantiation59, 50, 56
: , :
49instantiation64, 51
:
50instantiation64, 60
:
51instantiation59, 52, 56
: , :
52instantiation66, 53, 54
: , : , :
53instantiation55, 56, 57
: , :
54assumption
55theorem
proveit.numbers.number_sets.integers.int_interval_within_int
56instantiation66, 67, 58
: , : , :
57instantiation59, 60, 61
: , :
58theorem
proveit.numbers.numerals.decimals.nat1
59theorem
60instantiation66, 62, 63
: , : , :
61instantiation64, 65
:
62theorem
proveit.numbers.number_sets.integers.nat_pos_within_int
63theorem
proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
64theorem
proveit.numbers.negation.int_closure
65instantiation66, 67, 68
: , : , :
66theorem
proveit.logic.sets.inclusion.superset_membership_from_proper_subset
67theorem
proveit.numbers.number_sets.integers.nat_within_int
68theorem
proveit.numbers.numerals.decimals.nat2