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  ⊢  
  : , : , :
1reference11  ⊢  
2instantiation11, 3  ⊢  
  : , : , :
3instantiation4, 14, 24, 5, 6*  ⊢  
  : , :
4theorem  ⊢  
 proveit.numbers.division.div_as_mult
5instantiation7, 49  ⊢  
  :
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, 47, 18*  ⊢  
  : , :
13theorem  ⊢  
 proveit.numbers.multiplication.commutation
14instantiation50, 31, 19  ⊢  
  : , : , :
15instantiation50, 31, 20  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
17instantiation50, 21, 22  ⊢  
  : , : , :
18instantiation23, 24  ⊢  
  :
19instantiation25, 26, 27  ⊢  
  : , : , :
20instantiation50, 39, 28  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
22instantiation50, 29, 30  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
24instantiation50, 31, 32  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
26instantiation33, 34  ⊢  
  : , :
27axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
28instantiation50, 35, 36  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
30instantiation50, 37, 38  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
32instantiation50, 39, 40  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
34theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
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