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, 3  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
2instantiation60, 35, 4  ⊢  
  : , : , :
3instantiation12, 5, 6  ⊢  
  : , : , :
4instantiation60, 40, 7  ⊢  
  : , : , :
5instantiation28, 15, 8  ⊢  
  : , :
6instantiation9, 10, 11  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
8instantiation12, 13, 14  ⊢  
  : , : , :
9axiom  ⊢  
 proveit.logic.equality.equals_transitivity
10instantiation20, 62, 16, 21, 18, 22, 15, 29, 30, 24  ⊢  
  : , : , : , : , : , :
11instantiation20, 21, 57, 16, 22, 17, 18, 25, 26, 29, 30, 24  ⊢  
  : , : , : , : , : , :
12theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
13instantiation28, 19, 24  ⊢  
  : , :
14instantiation20, 21, 57, 62, 22, 23, 29, 30, 24  ⊢  
  : , : , : , : , : , :
15instantiation28, 25, 26  ⊢  
  : , :
16theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
17instantiation31  ⊢  
  : , :
18instantiation27  ⊢  
  : , : , :
19instantiation28, 29, 30  ⊢  
  : , :
20theorem  ⊢  
 proveit.numbers.multiplication.disassociation
21axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
22theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
23instantiation31  ⊢  
  : , :
24instantiation60, 35, 32  ⊢  
  : , : , :
25instantiation60, 35, 33  ⊢  
  : , : , :
26instantiation60, 35, 34  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
28theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
29theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
30instantiation60, 35, 36  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
32instantiation60, 38, 37  ⊢  
  : , : , :
33instantiation60, 38, 39  ⊢  
  : , : , :
34instantiation60, 40, 41  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
36theorem  ⊢  
 proveit.physics.quantum.QPE._phase_is_real
37instantiation60, 43, 42  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
39instantiation60, 43, 53  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
41theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
42instantiation60, 44, 45  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
44instantiation46, 47, 48  ⊢  
  : , :
45assumption  ⊢  
46theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
47theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
48instantiation49, 50, 51  ⊢  
  : , :
49theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
50instantiation52, 53, 54  ⊢  
  : , :
51instantiation55, 56  ⊢  
  :
52theorem  ⊢  
 proveit.numbers.exponentiation.exp_int_closure
53instantiation60, 61, 57  ⊢  
  : , : , :
54instantiation60, 58, 59  ⊢  
  : , : , :
55theorem  ⊢  
 proveit.numbers.negation.int_closure
56instantiation60, 61, 62  ⊢  
  : , : , :
57theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
58theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
59axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
60theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
61theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
62theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1