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  ⊢  
  :
1theorem  ⊢  
 proveit.numbers.negation.complex_closure
2instantiation3, 4, 5  ⊢  
  : , :
3theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
4instantiation63, 28, 6  ⊢  
  : , : , :
5instantiation7, 8, 9  ⊢  
  : , : , :
6instantiation63, 37, 10  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
8instantiation15, 16, 11  ⊢  
  : , :
9instantiation12, 13, 14  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
11instantiation15, 24, 25  ⊢  
  : , :
12axiom  ⊢  
 proveit.logic.equality.equals_transitivity
13instantiation17, 62, 49, 18, 21, 19, 16, 24, 25  ⊢  
  : , : , : , : , : , :
14instantiation17, 18, 49, 19, 20, 21, 22, 23, 24, 25  ⊢  
  : , : , : , : , : , :
15theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
16instantiation63, 28, 26  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.multiplication.disassociation
18axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
19theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
20instantiation27  ⊢  
  : , :
21instantiation27  ⊢  
  : , :
22instantiation63, 28, 31  ⊢  
  : , : , :
23instantiation63, 28, 32  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
25instantiation63, 28, 29  ⊢  
  : , : , :
26instantiation30, 31, 32  ⊢  
  : , :
27theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
28theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
29instantiation33, 34, 35  ⊢  
  : , :
30theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
31instantiation63, 47, 36  ⊢  
  : , : , :
32instantiation63, 37, 38  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
34instantiation39, 40, 41, 42  ⊢  
  : , : , :
35instantiation43, 44  ⊢  
  :
36instantiation63, 50, 45  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
38theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
39theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
41instantiation63, 47, 46  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
43theorem  ⊢  
 proveit.numbers.negation.real_closure
44instantiation63, 47, 48  ⊢  
  : , : , :
45instantiation63, 61, 49  ⊢  
  : , : , :
46instantiation63, 50, 58  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
48instantiation63, 50, 51  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
50theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
51instantiation63, 52, 53  ⊢  
  : , : , :
52instantiation54, 55, 60  ⊢  
  : , :
53assumption  ⊢  
54theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
55instantiation56, 57, 58  ⊢  
  : , :
56theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
57instantiation59, 60  ⊢  
  :
58instantiation63, 61, 62  ⊢  
  : , : , :
59theorem  ⊢  
 proveit.numbers.negation.int_closure
60instantiation63, 64, 65  ⊢  
  : , : , :
61theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
62theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
63theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
64theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
65theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos