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  ⊢  
  : , : , :
1reference15  ⊢  
2instantiation15, 3  ⊢  
  : , : , :
3instantiation15, 4  ⊢  
  : , : , :
4instantiation15, 5  ⊢  
  : , : , :
5instantiation6, 30, 7, 8, 9*  ⊢  
  : , :
6theorem  ⊢  
 proveit.numbers.division.div_as_mult
7instantiation49, 40, 10  ⊢  
  : , : , :
8instantiation27, 14  ⊢  
  :
9instantiation11, 12, 13  ⊢  
  : , : , :
10instantiation45, 46, 14  ⊢  
  : , : , :
11axiom  ⊢  
 proveit.logic.equality.equals_transitivity
12instantiation15, 16  ⊢  
  : , : , :
13instantiation17, 18  ⊢  
  :
14theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
15axiom  ⊢  
 proveit.logic.equality.substitution
16instantiation19, 24, 41, 20, 21, 22*  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
18instantiation23, 24, 25  ⊢  
  : , :
19theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
20instantiation26, 34  ⊢  
  :
21instantiation27, 28  ⊢  
  :
22instantiation29, 36, 30, 31*  ⊢  
  : , :
23theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
24instantiation49, 40, 32  ⊢  
  : , : , :
25instantiation33, 36  ⊢  
  :
26theorem  ⊢  
 proveit.numbers.negation.real_closure
27theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
28theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
29theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_right
30instantiation49, 40, 34  ⊢  
  : , : , :
31instantiation35, 36  ⊢  
  :
32instantiation49, 38, 37  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.negation.complex_closure
34instantiation49, 38, 39  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
36instantiation49, 40, 41  ⊢  
  : , : , :
37instantiation49, 43, 42  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
39instantiation49, 43, 44  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
41instantiation45, 46, 47  ⊢  
  : , : , :
42instantiation49, 50, 48  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
44instantiation49, 50, 51  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
46instantiation52, 53  ⊢  
  : , :
47axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
48theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
49theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
51theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
52theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
53theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements