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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  ⊢  
  : , : , :
1reference11  ⊢  
2instantiation11, 3  ⊢  
  : , : , :
3instantiation4, 14, 24, 5, 6*  ⊢  
  : , :
4theorem  ⊢  
 proveit.numbers.division.div_as_mult
5instantiation7, 46  ⊢  
  :
6instantiation8, 9, 10  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
8axiom  ⊢  
 proveit.logic.equality.equals_transitivity
9instantiation11, 12  ⊢  
  : , : , :
10instantiation13, 14, 15  ⊢  
  : , :
11axiom  ⊢  
 proveit.logic.equality.substitution
12instantiation16, 17, 44, 18*  ⊢  
  : , :
13theorem  ⊢  
 proveit.numbers.multiplication.commutation
14instantiation47, 30, 19  ⊢  
  : , : , :
15instantiation47, 30, 20  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
17instantiation47, 21, 22  ⊢  
  : , : , :
18instantiation23, 24  ⊢  
  :
19instantiation47, 25, 26  ⊢  
  : , : , :
20instantiation47, 36, 27  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
22instantiation47, 28, 29  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
24instantiation47, 30, 31  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
26theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
27instantiation47, 32, 33  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
29instantiation47, 34, 35  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
31instantiation47, 36, 37  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
33instantiation38, 39, 40  ⊢  
  : , :
34theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
35instantiation47, 41, 46  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
37instantiation47, 42, 43  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
39instantiation47, 45, 44  ⊢  
  : , : , :
40instantiation47, 45, 46  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
42theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
43instantiation47, 48, 49  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
45theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
46theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
47theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
49theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements