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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
0generalization1  ⊢  
1instantiation2, 3, 4, 5,  ⊢  
  : , :
2theorem  ⊢  
 proveit.numbers.division.div_real_closure
3instantiation58, 12, 6  ⊢  
  : , : , :
4instantiation7, 8, 60,  ⊢  
  : , :
5instantiation9, 10, 11,  ⊢  
  : , :
6instantiation58, 17, 47  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.numbers.exponentiation.exp_real_closure_nat_power
8instantiation58, 12, 13,  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
10instantiation58, 15, 14,  ⊢  
  : , : , :
11instantiation58, 15, 16  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
13instantiation58, 17, 21,  ⊢  
  : , : , :
14instantiation58, 19, 18,  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
16instantiation58, 19, 20  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
18instantiation34, 21, 22,  ⊢  
  :
19theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
20theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
21instantiation58, 23, 30,  ⊢  
  : , : , :
22instantiation40, 24, 25,  ⊢  
  : , : , :
23instantiation45, 28, 29  ⊢  
  : , :
24instantiation26, 27  ⊢  
  :
25instantiation46, 28, 29, 30,  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
27instantiation31, 32, 44  ⊢  
  : , :
28instantiation51, 35, 47  ⊢  
  : , :
29instantiation51, 52, 33  ⊢  
  : , :
30assumption  ⊢  
31theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_closure_bin
32instantiation34, 35, 36  ⊢  
  :
33instantiation58, 37, 38  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
35instantiation58, 39, 49  ⊢  
  : , : , :
36instantiation40, 41, 42  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.integers.neg_int_within_int
38instantiation43, 44  ⊢  
  :
39instantiation45, 47, 48  ⊢  
  : , :
40theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
41theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
42instantiation46, 47, 48, 49  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
44theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
45theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
46theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
47instantiation58, 59, 50  ⊢  
  : , : , :
48instantiation51, 52, 53  ⊢  
  : , :
49assumption  ⊢  
50theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
51theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
52instantiation58, 54, 55  ⊢  
  : , : , :
53instantiation56, 57  ⊢  
  :
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.numbers.negation.int_closure
57instantiation58, 59, 60  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
59theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
60theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2