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, 4, 5*  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.division.div_as_mult
2reference13  ⊢  
3reference23  ⊢  
4instantiation6, 48  ⊢  
  :
5instantiation7, 8, 9  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
7axiom  ⊢  
 proveit.logic.equality.equals_transitivity
8instantiation10, 11  ⊢  
  : , : , :
9instantiation12, 13, 14  ⊢  
  : , :
10axiom  ⊢  
 proveit.logic.equality.substitution
11instantiation15, 16, 46, 17*  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.multiplication.commutation
13instantiation49, 30, 18  ⊢  
  : , : , :
14instantiation49, 30, 19  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
16instantiation49, 20, 21  ⊢  
  : , : , :
17instantiation22, 23  ⊢  
  :
18instantiation24, 25, 26  ⊢  
  : , : , :
19instantiation49, 38, 27  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
21instantiation49, 28, 29  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
23instantiation49, 30, 31  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
25instantiation32, 33  ⊢  
  : , :
26axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
27instantiation49, 34, 35  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
29instantiation49, 36, 37  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
31instantiation49, 38, 39  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
33theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
34theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
35instantiation40, 41, 42  ⊢  
  : , :
36theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
37instantiation49, 43, 48  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
39instantiation49, 44, 45  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
41instantiation49, 47, 46  ⊢  
  : , : , :
42instantiation49, 47, 48  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
44theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
45instantiation49, 50, 51  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
47theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
48theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
49theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
51theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements