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
4instantiation54, 28, 6  ⊢  
  : , : , :
5instantiation7, 8, 9  ⊢  
  : , : , :
6instantiation54, 35, 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, 53, 56, 18, 21, 19, 16, 24, 25  ⊢  
  : , : , : , : , : , :
14instantiation17, 18, 56, 19, 20, 21, 22, 23, 24, 25  ⊢  
  : , : , : , : , : , :
15theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
16instantiation54, 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  ⊢  
  : , :
22instantiation54, 28, 43  ⊢  
  : , : , :
23instantiation54, 28, 31  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
25instantiation54, 28, 29  ⊢  
  : , : , :
26instantiation30, 43, 31  ⊢  
  : , :
27theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
28theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
29instantiation32, 33, 38, 34  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
31instantiation54, 35, 36  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
33instantiation37, 38  ⊢  
  :
34instantiation39, 40  ⊢  
  :
35theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
37theorem  ⊢  
 proveit.numbers.negation.real_closure
38instantiation41, 42, 43, 44  ⊢  
  : , :
39theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
40assumption  ⊢  
41theorem  ⊢  
 proveit.numbers.division.div_real_closure
42instantiation54, 46, 45  ⊢  
  : , : , :
43instantiation54, 46, 47  ⊢  
  : , : , :
44instantiation48, 49  ⊢  
  :
45instantiation54, 51, 50  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
47instantiation54, 51, 52  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
49theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
50instantiation54, 55, 53  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
52instantiation54, 55, 56  ⊢  
  : , : , :
53theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
54theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
55theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
56theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2