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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, 3, 4, 5, ,  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.numbers.number_sets.integers.int_not_in_interval
2instantiation48, 31, 47  ⊢  
  : , :
3reference50  ⊢  
4reference27  ⊢  
5instantiation6, 7, 8, ,  ⊢  
  : , :
6theorem  ⊢  
 proveit.logic.booleans.disjunction.or_if_only_left
7instantiation9, 10, 11,  ⊢  
  : , : , :
8instantiation12, 13, 14, 15  ⊢  
  : , :
9axiom  ⊢  
 proveit.numbers.ordering.transitivity_less_less
10assumption  ⊢  
11instantiation16, 17  ⊢  
  :
12theorem  ⊢  
 proveit.numbers.ordering.not_less_from_less_eq
13instantiation56, 18, 19  ⊢  
  : , : , :
14instantiation20, 21, 55  ⊢  
  : , : , :
15instantiation22, 39, 50, 34  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
17instantiation23, 24, 25  ⊢  
  : , :
18theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
19instantiation56, 26, 27  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
21instantiation28, 29  ⊢  
  : , :
22theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_upper_bound
23theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
24instantiation30, 31, 32  ⊢  
  :
25theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
26theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
27instantiation56, 33, 34  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
30theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
31instantiation56, 35, 45  ⊢  
  : , : , :
32instantiation36, 37, 38  ⊢  
  : , : , :
33instantiation42, 39, 50  ⊢  
  : , :
34instantiation40, 41  ⊢  
  : , :
35instantiation42, 47, 44  ⊢  
  : , :
36theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
37theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
38instantiation43, 47, 44, 45  ⊢  
  : , : , :
39instantiation48, 46, 47  ⊢  
  : , :
40theorem  ⊢  
 proveit.logic.booleans.conjunction.left_from_and
41assumption  ⊢  
42theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
43theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
44instantiation48, 50, 49  ⊢  
  : , :
45assumption  ⊢  
46instantiation52, 50  ⊢  
  :
47instantiation56, 57, 51  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
49instantiation52, 53  ⊢  
  :
50instantiation56, 54, 55  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
52theorem  ⊢  
 proveit.numbers.negation.int_closure
53instantiation56, 57, 58  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
55theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
56theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
57theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
58theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2