logo

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  ⊢  
  : , : , :
1reference11  ⊢  
2instantiation14, 4  ⊢  
  : , : , :
3instantiation14, 5  ⊢  
  : , : , :
4instantiation14, 6  ⊢  
  : , : , :
5instantiation14, 6  ⊢  
  : , : , :
6instantiation7, 17, 27, 8, 9*  ⊢  
  : , :
7theorem  ⊢  
 proveit.numbers.division.div_as_mult
8instantiation10, 49  ⊢  
  :
9instantiation11, 12, 13  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
11axiom  ⊢  
 proveit.logic.equality.equals_transitivity
12instantiation14, 15  ⊢  
  : , : , :
13instantiation16, 17, 18  ⊢  
  : , :
14axiom  ⊢  
 proveit.logic.equality.substitution
15instantiation19, 20, 47, 21*  ⊢  
  : , :
16theorem  ⊢  
 proveit.numbers.multiplication.commutation
17instantiation50, 33, 22  ⊢  
  : , : , :
18instantiation50, 33, 23  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
20instantiation50, 24, 25  ⊢  
  : , : , :
21instantiation26, 27  ⊢  
  :
22instantiation50, 28, 29  ⊢  
  : , : , :
23instantiation50, 39, 30  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
25instantiation50, 31, 32  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
27instantiation50, 33, 34  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
30instantiation50, 35, 36  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
32instantiation50, 37, 38  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
34instantiation50, 39, 40  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
36instantiation41, 42, 43  ⊢  
  : , :
37theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
38instantiation50, 44, 49  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
40instantiation50, 45, 46  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
42instantiation50, 48, 47  ⊢  
  : , : , :
43instantiation50, 48, 49  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
45theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
46instantiation50, 51, 52  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
48theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
49theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
50theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
51theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
52theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements