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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,  ⊢  
  : , : , :
1reference51  ⊢  
2theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
3instantiation4, 5, 6,  ⊢  
  :
4theorem  ⊢  
 proveit.numbers.exponentiation.sqrd_pos_closure
5instantiation51, 7, 8,  ⊢  
  : , : , :
6instantiation9, 13, 10, 11,  ⊢  
  : , :
7theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
8instantiation51, 12, 13,  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.ordering.less_is_not_eq_int
10theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
11instantiation14, 15, 16,  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
13instantiation51, 17, 19,  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_eq_less
15instantiation18, 22, 23, 19,  ⊢  
  : , : , :
16instantiation20, 21  ⊢  
  :
17instantiation38, 22, 23  ⊢  
  : , :
18theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_upper_bound
19assumption  ⊢  
20theorem  ⊢  
 proveit.numbers.number_sets.integers.negative_if_in_neg_int
21instantiation24, 25  ⊢  
  :
22instantiation44, 26, 40  ⊢  
  : , :
23instantiation49, 27  ⊢  
  :
24theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
25instantiation28, 29, 30  ⊢  
  : , :
26instantiation49, 45  ⊢  
  :
27instantiation44, 32, 40  ⊢  
  : , :
28theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
29instantiation31, 32, 33  ⊢  
  :
30theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
31theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
32instantiation51, 34, 42  ⊢  
  : , : , :
33instantiation35, 36, 37  ⊢  
  : , : , :
34instantiation38, 40, 41  ⊢  
  : , :
35theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
36theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
37instantiation39, 40, 41, 42  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
39theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
40instantiation51, 52, 43  ⊢  
  : , : , :
41instantiation44, 45, 46  ⊢  
  : , :
42assumption  ⊢  
43theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
44theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
45instantiation51, 47, 48  ⊢  
  : , : , :
46instantiation49, 50  ⊢  
  :
47theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
48theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
49theorem  ⊢  
 proveit.numbers.negation.int_closure
50instantiation51, 52, 53  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
52theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
53theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2