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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
2instantiation15, 4  ⊢  
  : , : , :
3instantiation15, 5  ⊢  
  : , : , :
4instantiation15, 7  ⊢  
  : , : , :
5instantiation15, 6  ⊢  
  : , : , :
6instantiation15, 7  ⊢  
  : , : , :
7instantiation8, 9, 10, 11  ⊢  
  : , : , : , :
8theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
9instantiation15, 12  ⊢  
  : , : , :
10instantiation13, 14  ⊢  
  : , :
11instantiation15, 16  ⊢  
  : , : , :
12instantiation17, 18, 19  ⊢  
  : , :
13theorem  ⊢  
 proveit.logic.equality.equals_reversal
14instantiation20, 21, 27, 26, 22  ⊢  
  : , : , :
15axiom  ⊢  
 proveit.logic.equality.substitution
16instantiation23, 24, 25  ⊢  
  : , :
17theorem  ⊢  
 proveit.numbers.addition.commutation
18instantiation53, 28, 26  ⊢  
  : , : , :
19instantiation53, 28, 27  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.exponentiation.product_of_real_powers
21instantiation53, 28, 29  ⊢  
  : , : , :
22instantiation30, 52  ⊢  
  :
23theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
24instantiation53, 31, 32  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
26instantiation33, 34, 35  ⊢  
  : , : , :
27instantiation53, 37, 36  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
29instantiation53, 37, 38  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
31theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
32instantiation53, 39, 40  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
34instantiation41, 42  ⊢  
  : , :
35axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
36instantiation53, 44, 43  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
38instantiation53, 44, 45  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
40instantiation53, 46, 47  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
42theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
43instantiation48, 49  ⊢  
  :
44theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
45instantiation53, 54, 50  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
47instantiation53, 51, 52  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.negation.int_closure
49instantiation53, 54, 55  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
51theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
52theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
53theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
54theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
55theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1