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  ⊢  
  : , : , :
1reference13  ⊢  
2instantiation17, 6  ⊢  
  : , : , :
3instantiation17, 4  ⊢  
  : , : , :
4instantiation17, 5  ⊢  
  : , : , :
5instantiation17, 6  ⊢  
  : , : , :
6instantiation17, 7  ⊢  
  : , : , :
7instantiation8, 32, 9, 10, 11*  ⊢  
  : , :
8theorem  ⊢  
 proveit.numbers.division.div_as_mult
9instantiation51, 42, 12  ⊢  
  : , : , :
10instantiation29, 16  ⊢  
  :
11instantiation13, 14, 15  ⊢  
  : , : , :
12instantiation47, 48, 16  ⊢  
  : , : , :
13axiom  ⊢  
 proveit.logic.equality.equals_transitivity
14instantiation17, 18  ⊢  
  : , : , :
15instantiation19, 20  ⊢  
  :
16theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
17axiom  ⊢  
 proveit.logic.equality.substitution
18instantiation21, 26, 43, 22, 23, 24*  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
20instantiation25, 26, 27  ⊢  
  : , :
21theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
22instantiation28, 36  ⊢  
  :
23instantiation29, 30  ⊢  
  :
24instantiation31, 38, 32, 33*  ⊢  
  : , :
25theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
26instantiation51, 42, 34  ⊢  
  : , : , :
27instantiation35, 38  ⊢  
  :
28theorem  ⊢  
 proveit.numbers.negation.real_closure
29theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
30theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
31theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_right
32instantiation51, 42, 36  ⊢  
  : , : , :
33instantiation37, 38  ⊢  
  :
34instantiation51, 40, 39  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.negation.complex_closure
36instantiation51, 40, 41  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
38instantiation51, 42, 43  ⊢  
  : , : , :
39instantiation51, 45, 44  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
41instantiation51, 45, 46  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
43instantiation47, 48, 49  ⊢  
  : , : , :
44instantiation51, 52, 50  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
46instantiation51, 52, 53  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
48instantiation54, 55  ⊢  
  : , :
49axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
50theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
51theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
52theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
53theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
54theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
55theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements