logo

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  ⊢  
  : , :
1reference11  ⊢  
2instantiation3, 4, 5, 6  ⊢  
  : , : , : , :
3theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
4instantiation26, 61, 7, 8, 9*  ⊢  
  : , :
5instantiation10  ⊢  
  :
6instantiation11, 12  ⊢  
  : , :
7instantiation13, 57, 51  ⊢  
  : , :
8instantiation14, 105, 15, 46, 16  ⊢  
  : , :
9instantiation23, 17, 18  ⊢  
  : , : , :
10axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
11theorem  ⊢  
 proveit.logic.equality.equals_reversal
12instantiation21, 19  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
14theorem  ⊢  
 proveit.numbers.multiplication.mult_not_eq_zero
15instantiation48  ⊢  
  : , :
16instantiation103, 54, 20  ⊢  
  : , : , :
17instantiation21, 22  ⊢  
  : , : , :
18instantiation23, 24, 25  ⊢  
  : , : , :
19instantiation26, 61, 51, 32, 27*  ⊢  
  : , :
20instantiation103, 64, 28  ⊢  
  : , : , :
21axiom  ⊢  
 proveit.logic.equality.substitution
22instantiation29, 57, 51, 30, 31, 32, 33*  ⊢  
  : , : , :
23axiom  ⊢  
 proveit.logic.equality.equals_transitivity
24instantiation34, 95, 105, 36, 38, 37, 61, 39, 41  ⊢  
  : , : , : , : , : , :
25instantiation35, 36, 105, 37, 38, 39, 41  ⊢  
  : , : , : , :
26theorem  ⊢  
 proveit.numbers.division.div_as_mult
27instantiation40, 41  ⊢  
  :
28instantiation103, 75, 42  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_product
30instantiation43, 71  ⊢  
  :
31instantiation44, 88  ⊢  
  :
32instantiation44, 53  ⊢  
  :
33instantiation45, 46, 86, 47*  ⊢  
  : , :
34theorem  ⊢  
 proveit.numbers.multiplication.disassociation
35theorem  ⊢  
 proveit.numbers.multiplication.elim_one_any
36axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
37theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
38instantiation48  ⊢  
  : , :
39instantiation103, 70, 49  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
41instantiation50, 51, 52  ⊢  
  : , :
42instantiation103, 85, 53  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.negation.real_closure
44theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
45theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
46instantiation103, 54, 55  ⊢  
  : , : , :
47instantiation56, 57  ⊢  
  :
48theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
49instantiation103, 82, 58  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
51instantiation103, 70, 59  ⊢  
  : , : , :
52instantiation60, 61  ⊢  
  :
53instantiation62, 81, 63  ⊢  
  :
54theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
55instantiation103, 64, 65  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
57instantiation103, 70, 66  ⊢  
  : , : , :
58instantiation103, 67, 68  ⊢  
  : , : , :
59instantiation103, 82, 69  ⊢  
  : , : , :
60theorem  ⊢  
 proveit.numbers.negation.complex_closure
61instantiation103, 70, 71  ⊢  
  : , : , :
62theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
63instantiation72, 73, 74  ⊢  
  : , : , :
64theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
65instantiation103, 75, 76  ⊢  
  : , : , :
66instantiation103, 82, 77  ⊢  
  : , : , :
67theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
68instantiation78, 79, 80  ⊢  
  : , :
69instantiation103, 91, 81  ⊢  
  : , : , :
70theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
71instantiation103, 82, 83  ⊢  
  : , : , :
72theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
73theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
74instantiation84, 93, 94, 90  ⊢  
  : , : , :
75theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
76instantiation103, 85, 88  ⊢  
  : , : , :
77instantiation103, 91, 102  ⊢  
  : , : , :
78theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
79instantiation103, 87, 86  ⊢  
  : , : , :
80instantiation103, 87, 88  ⊢  
  : , : , :
81instantiation103, 89, 90  ⊢  
  : , : , :
82theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
83instantiation103, 91, 93  ⊢  
  : , : , :
84theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
85theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
86theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
87theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
88theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
89instantiation92, 93, 94  ⊢  
  : , :
90assumption  ⊢  
91theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
92theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
93instantiation103, 104, 95  ⊢  
  : , : , :
94instantiation96, 97, 98  ⊢  
  : , :
95theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
96theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
97instantiation103, 99, 100  ⊢  
  : , : , :
98instantiation101, 102  ⊢  
  :
99theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
100theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
101theorem  ⊢  
 proveit.numbers.negation.int_closure
102instantiation103, 104, 105  ⊢  
  : , : , :
103theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
104theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
105theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements