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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, 31, 9, 10, 11*  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
7instantiation12, 13, 14  ⊢  
  : , :
8theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
9instantiation46, 35, 15  ⊢  
  : , : , :
10instantiation16, 48  ⊢  
  :
11instantiation17, 25, 18, 19*  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
13instantiation46, 30, 20  ⊢  
  : , : , :
14instantiation46, 30, 21  ⊢  
  : , : , :
15instantiation46, 33, 22  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
17theorem  ⊢  
 proveit.numbers.negation.pos_times_neg
18instantiation46, 30, 23  ⊢  
  : , : , :
19instantiation24, 25  ⊢  
  :
20instantiation46, 35, 26  ⊢  
  : , : , :
21instantiation27, 31  ⊢  
  :
22instantiation28, 34  ⊢  
  :
23instantiation46, 35, 29  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
25instantiation46, 30, 31  ⊢  
  : , : , :
26instantiation46, 33, 32  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.negation.real_closure
28theorem  ⊢  
 proveit.numbers.negation.int_closure
29instantiation46, 33, 34  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
31instantiation46, 35, 36  ⊢  
  : , : , :
32instantiation46, 38, 37  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
34instantiation46, 38, 39  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
36instantiation46, 40, 41  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
38theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
39theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
40theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
41instantiation42, 43, 44  ⊢  
  : , :
42theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
43instantiation46, 47, 45  ⊢  
  : , : , :
44instantiation46, 47, 48  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
46theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
47theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
48theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
*equality replacement requirements