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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, ,  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.substitution
2instantiation3, 4, ,  ⊢  
  : , :
3theorem  ⊢  
 proveit.logic.equality.equals_reversal
4instantiation5, 9, 14, 6, 7, 8*, ,  ⊢  
  : , : , :
5theorem  ⊢  
 proveit.numbers.division.mult_frac_left
6instantiation29, 9, 10  ⊢  
  : , :
7instantiation11, 12  ⊢  
  : , :
8instantiation13, 14,  ⊢  
  :
9instantiation49, 34, 15  ⊢  
  : , : , :
10instantiation22, 26  ⊢  
  :
11theorem  ⊢  
 proveit.numbers.addition.subtraction.nonzero_difference_if_different
12instantiation16, 17  ⊢  
  : , :
13theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
14instantiation29, 18, 19,  ⊢  
  : , :
15instantiation49, 39, 20  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
17assumption  ⊢  
18instantiation25, 26, 21,  ⊢  
  : , :
19instantiation22, 23,  ⊢  
  :
20instantiation49, 45, 38  ⊢  
  : , : , :
21instantiation49, 34, 24  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.negation.complex_closure
23instantiation25, 26, 27,  ⊢  
  : , :
24instantiation49, 39, 28  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
26assumption  ⊢  
27instantiation29, 30, 31  ⊢  
  : , :
28instantiation49, 45, 32  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.addition.add_complex_closure_bin
30instantiation49, 34, 33  ⊢  
  : , : , :
31instantiation49, 34, 35  ⊢  
  : , : , :
32instantiation36, 37, 38  ⊢  
  : , :
33instantiation49, 39, 40  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
35instantiation41, 42, 43  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
37instantiation49, 50, 43  ⊢  
  : , : , :
38instantiation49, 50, 44  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
40instantiation49, 45, 46  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
42instantiation47, 48  ⊢  
  : , :
43assumption  ⊢  
44theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
45theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
46instantiation49, 50, 51  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
48theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_within_real
49theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
51theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements