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
2instantiation51, 33, 6  ⊢  
  : , : , :
3instantiation51, 33, 7  ⊢  
  : , : , :
4instantiation17, 14  ⊢  
  :
5instantiation8, 9, 34, 10, 11, 12*  ⊢  
  : , : , :
6instantiation51, 31, 13  ⊢  
  : , : , :
7instantiation39, 40, 14  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
9instantiation51, 33, 15  ⊢  
  : , : , :
10instantiation51, 31, 16  ⊢  
  : , : , :
11instantiation17, 18  ⊢  
  :
12instantiation19, 27, 20, 21*  ⊢  
  : , :
13instantiation51, 38, 22  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
15instantiation51, 31, 23  ⊢  
  : , : , :
16instantiation51, 38, 24  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
18theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
19theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_right
20instantiation51, 33, 25  ⊢  
  : , : , :
21instantiation26, 27  ⊢  
  :
22instantiation51, 28, 29  ⊢  
  : , : , :
23instantiation51, 38, 30  ⊢  
  : , : , :
24instantiation47, 44  ⊢  
  :
25instantiation51, 31, 32  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
27instantiation51, 33, 34  ⊢  
  : , : , :
28instantiation35, 36, 48  ⊢  
  : , :
29assumption  ⊢  
30instantiation51, 49, 37  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
32instantiation51, 38, 44  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
34instantiation39, 40, 41  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
36instantiation42, 43, 44  ⊢  
  : , :
37theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
38theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
39theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
40instantiation45, 46  ⊢  
  : , :
41axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
42theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
43instantiation47, 48  ⊢  
  :
44instantiation51, 49, 50  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
46theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
47theorem  ⊢  
 proveit.numbers.negation.int_closure
48instantiation51, 52, 53  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
50theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
51theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
52theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
53theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements