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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  ⊢  
  : , : , :
1reference5  ⊢  
2instantiation5, 3  ⊢  
  : , : , :
3instantiation5, 4  ⊢  
  : , : , :
4instantiation5, 6  ⊢  
  : , : , :
5axiom  ⊢  
 proveit.logic.equality.substitution
6instantiation7, 8, 9, 10, 11*  ⊢  
  : , :
7theorem  ⊢  
 proveit.numbers.division.div_as_mult
8instantiation57, 39, 12  ⊢  
  : , : , :
9instantiation57, 39, 13  ⊢  
  : , : , :
10instantiation23, 20  ⊢  
  :
11instantiation14, 15, 40, 16, 17, 18*  ⊢  
  : , : , :
12instantiation57, 37, 19  ⊢  
  : , : , :
13instantiation45, 46, 20  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
15instantiation57, 39, 21  ⊢  
  : , : , :
16instantiation57, 37, 22  ⊢  
  : , : , :
17instantiation23, 24  ⊢  
  :
18instantiation25, 33, 26, 27*  ⊢  
  : , :
19instantiation57, 44, 28  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
21instantiation57, 37, 29  ⊢  
  : , : , :
22instantiation57, 44, 30  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
24theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
25theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_right
26instantiation57, 39, 31  ⊢  
  : , : , :
27instantiation32, 33  ⊢  
  :
28instantiation57, 34, 35  ⊢  
  : , : , :
29instantiation57, 44, 36  ⊢  
  : , : , :
30instantiation53, 50  ⊢  
  :
31instantiation57, 37, 38  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
33instantiation57, 39, 40  ⊢  
  : , : , :
34instantiation41, 42, 54  ⊢  
  : , :
35assumption  ⊢  
36instantiation57, 55, 43  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
38instantiation57, 44, 50  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
40instantiation45, 46, 47  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
42instantiation48, 49, 50  ⊢  
  : , :
43theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
44theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
45theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
46instantiation51, 52  ⊢  
  : , :
47axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
48theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
49instantiation53, 54  ⊢  
  :
50instantiation57, 55, 56  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
52theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
53theorem  ⊢  
 proveit.numbers.negation.int_closure
54instantiation57, 58, 59  ⊢  
  : , : , :
55theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
56theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
57theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
59theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements