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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  ⊢  
  : , : , :
1reference13  ⊢  
2instantiation13, 3  ⊢  
  : , : , :
3instantiation4, 28, 5, 6, 7*  ⊢  
  : , :
4theorem  ⊢  
 proveit.numbers.division.div_as_mult
5instantiation47, 38, 8  ⊢  
  : , : , :
6instantiation25, 12  ⊢  
  :
7instantiation9, 10, 11  ⊢  
  : , : , :
8instantiation43, 44, 12  ⊢  
  : , : , :
9axiom  ⊢  
 proveit.logic.equality.equals_transitivity
10instantiation13, 14  ⊢  
  : , : , :
11instantiation15, 16  ⊢  
  :
12theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
13axiom  ⊢  
 proveit.logic.equality.substitution
14instantiation17, 22, 39, 18, 19, 20*  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
16instantiation21, 22, 23  ⊢  
  : , :
17theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_real_power
18instantiation24, 32  ⊢  
  :
19instantiation25, 26  ⊢  
  :
20instantiation27, 34, 28, 29*  ⊢  
  : , :
21theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
22instantiation47, 38, 30  ⊢  
  : , : , :
23instantiation31, 34  ⊢  
  :
24theorem  ⊢  
 proveit.numbers.negation.real_closure
25theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
26theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
27theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_right
28instantiation47, 38, 32  ⊢  
  : , : , :
29instantiation33, 34  ⊢  
  :
30instantiation47, 36, 35  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.negation.complex_closure
32instantiation47, 36, 37  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
34instantiation47, 38, 39  ⊢  
  : , : , :
35instantiation47, 41, 40  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
37instantiation47, 41, 42  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
39instantiation43, 44, 45  ⊢  
  : , : , :
40instantiation47, 48, 46  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
42instantiation47, 48, 49  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
44instantiation50, 51  ⊢  
  : , :
45axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
46theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
47theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
49theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
50theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
51theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
*equality replacement requirements