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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, 4, 5, 6*, ,  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.numbers.division.mult_frac_left
2reference7  ⊢  
3reference12,  ⊢  
4instantiation27, 7, 8  ⊢  
  : , :
5instantiation9, 10  ⊢  
  : , :
6instantiation11, 12,  ⊢  
  :
7instantiation47, 32, 13  ⊢  
  : , : , :
8instantiation20, 24  ⊢  
  :
9theorem  ⊢  
 proveit.numbers.addition.subtraction.nonzero_difference_if_different
10instantiation14, 15  ⊢  
  : , :
11theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
12instantiation27, 16, 17,  ⊢  
  : , :
13instantiation47, 37, 18  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
15assumption  ⊢  
16instantiation23, 24, 19,  ⊢  
  : , :
17instantiation20, 21,  ⊢  
  :
18instantiation47, 43, 36  ⊢  
  : , : , :
19instantiation47, 32, 22  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.negation.complex_closure
21instantiation23, 24, 25,  ⊢  
  : , :
22instantiation47, 37, 26  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
24assumption  ⊢  
25instantiation27, 28, 29  ⊢  
  : , :
26instantiation47, 43, 30  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.addition.add_complex_closure_bin
28instantiation47, 32, 31  ⊢  
  : , : , :
29instantiation47, 32, 33  ⊢  
  : , : , :
30instantiation34, 35, 36  ⊢  
  : , :
31instantiation47, 37, 38  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
33instantiation39, 40, 41  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
35instantiation47, 48, 41  ⊢  
  : , : , :
36instantiation47, 48, 42  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
38instantiation47, 43, 44  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
40instantiation45, 46  ⊢  
  : , :
41assumption  ⊢  
42theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
43theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
44instantiation47, 48, 49  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
46theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_within_real
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