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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
2instantiation4, 5  ⊢  
  : , : , :
3instantiation6, 7  ⊢  
  :
4axiom  ⊢  
 proveit.logic.equality.substitution
5instantiation8, 13, 32, 9, 10, 11*  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
7instantiation12, 13, 14  ⊢  
  : , :
8theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
9instantiation40, 29, 15  ⊢  
  : , : , :
10instantiation16, 17  ⊢  
  :
11instantiation18, 26, 19, 20*  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
13instantiation40, 31, 21  ⊢  
  : , : , :
14instantiation22, 26  ⊢  
  :
15instantiation40, 34, 23  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
17theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
18theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_right
19instantiation40, 31, 24  ⊢  
  : , : , :
20instantiation25, 26  ⊢  
  :
21instantiation40, 29, 27  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.negation.complex_closure
23instantiation28, 35  ⊢  
  :
24instantiation40, 29, 30  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
26instantiation40, 31, 32  ⊢  
  : , : , :
27instantiation40, 34, 33  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.negation.int_closure
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
30instantiation40, 34, 35  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
32instantiation36, 37, 38  ⊢  
  : , : , :
33instantiation40, 41, 39  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
35instantiation40, 41, 42  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
37instantiation43, 44  ⊢  
  : , :
38axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
39theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
40theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
41theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
42theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
43theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
44theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements