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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  ⊢  
  : , :
1theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
2instantiation52, 20, 4  ⊢  
  : , : , :
3instantiation5, 6, 7, 8  ⊢  
  : , :
4instantiation52, 9, 10  ⊢  
  : , : , :
5theorem  ⊢  
 proveit.numbers.division.div_real_closure
6instantiation52, 20, 11  ⊢  
  : , : , :
7instantiation12, 13, 54  ⊢  
  : , :
8instantiation14, 15, 16  ⊢  
  : , :
9theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
10instantiation17, 18, 19  ⊢  
  : , :
11instantiation52, 28, 41  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
13instantiation52, 20, 21  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
15instantiation52, 23, 22  ⊢  
  : , : , :
16instantiation52, 23, 24  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
18instantiation52, 26, 25  ⊢  
  : , : , :
19instantiation52, 26, 27  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
21instantiation52, 28, 33  ⊢  
  : , : , :
22instantiation52, 30, 29  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
24instantiation52, 30, 31  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
26theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
27theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat4
28theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
29instantiation32, 33, 34  ⊢  
  :
30theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
31theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
32theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
33instantiation52, 35, 43  ⊢  
  : , : , :
34instantiation36, 37, 38  ⊢  
  : , : , :
35instantiation39, 41, 42  ⊢  
  : , :
36theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
37theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
38instantiation40, 41, 42, 43  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
40theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
41instantiation52, 53, 44  ⊢  
  : , : , :
42instantiation45, 46, 47  ⊢  
  : , :
43assumption  ⊢  
44theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
45theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
46instantiation52, 48, 49  ⊢  
  : , : , :
47instantiation50, 51  ⊢  
  :
48theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
49theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
50theorem  ⊢  
 proveit.numbers.negation.int_closure
51instantiation52, 53, 54  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
53theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
54theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2