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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  ⊢  
  : , : , :
1reference6  ⊢  
2instantiation6, 3  ⊢  
  : , : , :
3instantiation6, 4  ⊢  
  : , : , :
4instantiation6, 5  ⊢  
  : , : , :
5instantiation6, 7  ⊢  
  : , : , :
6axiom  ⊢  
 proveit.logic.equality.substitution
7instantiation8, 9, 10, 11, 12*  ⊢  
  : , :
8theorem  ⊢  
 proveit.numbers.division.div_as_mult
9instantiation58, 40, 13  ⊢  
  : , : , :
10instantiation58, 40, 14  ⊢  
  : , : , :
11instantiation24, 21  ⊢  
  :
12instantiation15, 16, 41, 17, 18, 19*  ⊢  
  : , : , :
13instantiation58, 38, 20  ⊢  
  : , : , :
14instantiation46, 47, 21  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
16instantiation58, 40, 22  ⊢  
  : , : , :
17instantiation58, 38, 23  ⊢  
  : , : , :
18instantiation24, 25  ⊢  
  :
19instantiation26, 34, 27, 28*  ⊢  
  : , :
20instantiation58, 45, 29  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
22instantiation58, 38, 30  ⊢  
  : , : , :
23instantiation58, 45, 31  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
25theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
26theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_right
27instantiation58, 40, 32  ⊢  
  : , : , :
28instantiation33, 34  ⊢  
  :
29instantiation58, 35, 36  ⊢  
  : , : , :
30instantiation58, 45, 37  ⊢  
  : , : , :
31instantiation54, 51  ⊢  
  :
32instantiation58, 38, 39  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
34instantiation58, 40, 41  ⊢  
  : , : , :
35instantiation42, 43, 55  ⊢  
  : , :
36assumption  ⊢  
37instantiation58, 56, 44  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
39instantiation58, 45, 51  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
41instantiation46, 47, 48  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
43instantiation49, 50, 51  ⊢  
  : , :
44theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
45theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
46theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
47instantiation52, 53  ⊢  
  : , :
48axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
49theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
50instantiation54, 55  ⊢  
  :
51instantiation58, 56, 57  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
53theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
54theorem  ⊢  
 proveit.numbers.negation.int_closure
55instantiation58, 59, 60  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
57theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
58theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
59theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
60theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements