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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  ⊢  
  : , :
1theorem  ⊢  
 proveit.logic.equality.equals_reversal
2instantiation3, 11, 24, 20, 4*  ⊢  
  : , :
3theorem  ⊢  
 proveit.numbers.division.div_as_mult
4instantiation5, 6, 7  ⊢  
  : , : , :
5axiom  ⊢  
 proveit.logic.equality.equals_transitivity
6instantiation8, 9  ⊢  
  : , : , :
7instantiation10, 11, 12  ⊢  
  : , :
8axiom  ⊢  
 proveit.logic.equality.substitution
9instantiation13, 14, 15, 16*  ⊢  
  : , :
10theorem  ⊢  
 proveit.numbers.multiplication.commutation
11instantiation47, 32, 17  ⊢  
  : , : , :
12instantiation18, 19, 24, 20  ⊢  
  : , :
13theorem  ⊢  
 proveit.numbers.exponentiation.neg_power_as_div
14instantiation47, 21, 22  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
16instantiation23, 24  ⊢  
  :
17instantiation25, 26, 27  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.division.div_complex_closure
19instantiation47, 32, 28  ⊢  
  : , : , :
20instantiation29, 43  ⊢  
  :
21theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
22instantiation47, 30, 31  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
24instantiation47, 32, 33  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
26instantiation34, 35  ⊢  
  : , :
27theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
28instantiation47, 39, 36  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
30theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
31instantiation47, 37, 38  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
33instantiation47, 39, 40  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
35theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
36instantiation47, 44, 41  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
38instantiation47, 42, 43  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
40instantiation47, 44, 45  ⊢  
  : , : , :
41instantiation47, 48, 46  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
43theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
44theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
45instantiation47, 48, 49  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
47theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
49theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements