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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, 6  ⊢  
  : , :
3theorem  ⊢  
 proveit.numbers.division.div_complex_closure
4instantiation7, 8, 9  ⊢  
  : , : , :
5instantiation56, 31, 10  ⊢  
  : , : , :
6instantiation11, 53  ⊢  
  :
7theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
8instantiation25, 17, 12  ⊢  
  : , :
9instantiation13, 14, 15  ⊢  
  : , : , :
10instantiation56, 34, 16  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
12instantiation25, 23, 24  ⊢  
  : , :
13axiom  ⊢  
 proveit.logic.equality.equals_transitivity
14instantiation18, 58, 43, 19, 22, 20, 17, 23, 24  ⊢  
  : , : , : , : , : , :
15instantiation18, 19, 43, 20, 21, 22, 26, 27, 23, 24  ⊢  
  : , : , : , : , : , :
16instantiation56, 39, 50  ⊢  
  : , : , :
17instantiation25, 26, 27  ⊢  
  : , :
18theorem  ⊢  
 proveit.numbers.multiplication.disassociation
19axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
20theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
21instantiation28  ⊢  
  : , :
22instantiation28  ⊢  
  : , :
23theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
24instantiation56, 31, 29  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
26instantiation56, 31, 30  ⊢  
  : , : , :
27instantiation56, 31, 32  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
29instantiation56, 34, 33  ⊢  
  : , : , :
30instantiation56, 34, 35  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
32instantiation56, 36, 37  ⊢  
  : , : , :
33instantiation56, 39, 38  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
35instantiation56, 39, 40  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
37theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
38instantiation56, 41, 42  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
40instantiation56, 57, 43  ⊢  
  : , : , :
41instantiation44, 45, 46  ⊢  
  : , :
42instantiation47, 48, 53  ⊢  
  : , :
43theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
44theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
45theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
46instantiation49, 50, 51  ⊢  
  : , :
47theorem  ⊢  
 proveit.numbers.modular.mod_natpos_in_interval
48assumption  ⊢  
49theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
50instantiation56, 52, 53  ⊢  
  : , : , :
51instantiation54, 55  ⊢  
  :
52theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
53theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
54theorem  ⊢  
 proveit.numbers.negation.int_closure
55instantiation56, 57, 58  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
57theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
58theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1