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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  ⊢  
  : , :
1reference10  ⊢  
2instantiation12, 3  ⊢  
  : , : , :
3instantiation12, 4  ⊢  
  : , : , :
4instantiation5, 6, 7, 8  ⊢  
  : , : , : , :
5theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
6instantiation12, 9  ⊢  
  : , : , :
7instantiation10, 11  ⊢  
  : , :
8instantiation12, 13  ⊢  
  : , : , :
9instantiation14, 15, 16  ⊢  
  : , :
10theorem  ⊢  
 proveit.logic.equality.equals_reversal
11instantiation17, 18, 19, 24, 20  ⊢  
  : , : , :
12axiom  ⊢  
 proveit.logic.equality.substitution
13instantiation21, 22, 23  ⊢  
  : , :
14theorem  ⊢  
 proveit.numbers.addition.commutation
15instantiation52, 35, 24  ⊢  
  : , : , :
16instantiation25, 26  ⊢  
  :
17theorem  ⊢  
 proveit.numbers.exponentiation.product_of_real_powers
18instantiation52, 35, 27  ⊢  
  : , : , :
19instantiation28, 36  ⊢  
  :
20instantiation29, 51  ⊢  
  :
21theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
22instantiation52, 30, 31  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
24instantiation32, 33, 34  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.negation.complex_closure
26instantiation52, 35, 36  ⊢  
  : , : , :
27instantiation52, 42, 37  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.negation.real_closure
29theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
30theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
31instantiation52, 38, 39  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
33instantiation40, 41  ⊢  
  : , :
34axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
35theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
36instantiation52, 42, 43  ⊢  
  : , : , :
37instantiation52, 47, 44  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
39instantiation52, 45, 46  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
41theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
42theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
43instantiation52, 47, 48  ⊢  
  : , : , :
44instantiation52, 53, 49  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
46instantiation52, 50, 51  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
48instantiation52, 53, 54  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
50theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
51theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
52theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
53theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
54theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1