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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, ,  ⊢  
  :
1theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
2instantiation23, 3, 4, ,  ⊢  
  :
3instantiation40, 5, 6,  ⊢  
  : , :
4instantiation7, 8,  ⊢  
  : , :
5instantiation47, 9, 20  ⊢  
  : , : , :
6instantiation47, 10, 11  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.numbers.addition.subtraction.pos_difference
8instantiation12, 13, 14,  ⊢  
  : , : , :
9instantiation34, 15, 41  ⊢  
  : , :
10theorem  ⊢  
 proveit.numbers.number_sets.integers.neg_int_within_int
11instantiation16, 17  ⊢  
  :
12theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
13instantiation18, 27  ⊢  
  : , :
14instantiation19, 20, 21*,  ⊢  
  :
15instantiation40, 22, 36  ⊢  
  : , :
16theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
17instantiation23, 24, 25  ⊢  
  :
18theorem  ⊢  
 proveit.logic.booleans.conjunction.right_from_and
19theorem  ⊢  
 proveit.physics.quantum.QPE._modabs_in_full_domain_simp
20instantiation26, 27  ⊢  
  : , :
21instantiation28, 29  ⊢  
  :
22instantiation45, 41  ⊢  
  :
23theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
24instantiation47, 30, 38  ⊢  
  : , : , :
25instantiation31, 32, 33  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.logic.booleans.conjunction.left_from_and
27assumption  ⊢  
28theorem  ⊢  
 proveit.numbers.absolute_value.abs_non_neg_elim
29assumption  ⊢  
30instantiation34, 36, 37  ⊢  
  : , :
31theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
32theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
33instantiation35, 36, 37, 38  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
35theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
36instantiation47, 48, 39  ⊢  
  : , : , :
37instantiation40, 41, 42  ⊢  
  : , :
38assumption  ⊢  
39theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
40theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
41instantiation47, 43, 44  ⊢  
  : , : , :
42instantiation45, 46  ⊢  
  :
43theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
44theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
45theorem  ⊢  
 proveit.numbers.negation.int_closure
46instantiation47, 48, 49  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
49theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements