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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  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.equals_transitivity
2instantiation4, 5  ⊢  
  : , : , :
3instantiation6, 7  ⊢  
  :
4axiom  ⊢  
 proveit.logic.equality.substitution
5instantiation8, 13, 35, 9, 10, 11*  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
7instantiation12, 13, 14  ⊢  
  : , :
8theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
9instantiation15, 25  ⊢  
  :
10instantiation16, 17  ⊢  
  :
11instantiation18, 27, 19, 20*  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
13instantiation54, 34, 21  ⊢  
  : , : , :
14instantiation54, 34, 22  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.negation.real_closure
16theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
17instantiation23, 36, 24  ⊢  
  :
18theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_right
19instantiation54, 34, 25  ⊢  
  : , : , :
20instantiation26, 27  ⊢  
  :
21instantiation54, 38, 28  ⊢  
  : , : , :
22instantiation54, 38, 29  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.number_sets.integers.pos_int_is_natural_pos
24instantiation30, 31, 32  ⊢  
  : , : , :
25instantiation54, 38, 33  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
27instantiation54, 34, 35  ⊢  
  : , : , :
28instantiation54, 42, 36  ⊢  
  : , : , :
29instantiation54, 42, 49  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.ordering.transitivity_less_less_eq
31theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
32instantiation37, 44, 45, 41  ⊢  
  : , : , :
33instantiation54, 42, 44  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
35instantiation54, 38, 39  ⊢  
  : , : , :
36instantiation54, 40, 41  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.integers.interval_lower_bound
38theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
39instantiation54, 42, 53  ⊢  
  : , : , :
40instantiation43, 44, 45  ⊢  
  : , :
41assumption  ⊢  
42theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
43theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
44instantiation54, 55, 46  ⊢  
  : , : , :
45instantiation47, 48, 49  ⊢  
  : , :
46theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
47theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
48instantiation54, 50, 51  ⊢  
  : , : , :
49instantiation52, 53  ⊢  
  :
50theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
51theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
52theorem  ⊢  
 proveit.numbers.negation.int_closure
53instantiation54, 55, 56  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
55theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
56theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements