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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, 3  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.equals_transitivity
2instantiation5, 7, 6, 48, 10, 8, 11, 21, 12, 4  ⊢  
  : , : , : , : , : , :
3instantiation5, 6, 43, 7, 8, 9, 10, 11, 21, 12, 14, 15  ⊢  
  : , : , : , : , : , :
4instantiation13, 14, 15  ⊢  
  : , :
5theorem  ⊢  
 proveit.numbers.multiplication.disassociation
6theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
7axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
8instantiation16  ⊢  
  : , : , :
9instantiation17  ⊢  
  : , :
10theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
11instantiation46, 30, 27  ⊢  
  : , : , :
12instantiation46, 30, 18  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
14instantiation46, 30, 19  ⊢  
  : , : , :
15instantiation20, 21, 22  ⊢  
  : , :
16theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
17theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
18instantiation23, 24  ⊢  
  :
19instantiation25, 26, 27, 28  ⊢  
  : , :
20theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
21instantiation46, 30, 29  ⊢  
  : , : , :
22instantiation46, 30, 31  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.physics.quantum.QPE._delta_b_is_real
24theorem  ⊢  
 proveit.physics.quantum.QPE._best_round_is_int
25theorem  ⊢  
 proveit.numbers.division.div_real_closure
26instantiation46, 38, 32  ⊢  
  : , : , :
27instantiation46, 38, 33  ⊢  
  : , : , :
28instantiation34, 35  ⊢  
  :
29instantiation46, 36, 37  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
31instantiation46, 38, 39  ⊢  
  : , : , :
32instantiation46, 41, 45  ⊢  
  : , : , :
33instantiation46, 41, 40  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
35theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
37theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
38theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
39instantiation46, 41, 42  ⊢  
  : , : , :
40instantiation46, 47, 43  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
42instantiation44, 45  ⊢  
  :
43theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
44theorem  ⊢  
 proveit.numbers.negation.int_closure
45instantiation46, 47, 48  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
47theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
48theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1