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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  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
2instantiation4, 23, 5, 6*, 7*  ⊢  
  : , :
3instantiation8, 9  ⊢  
  :
4theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.complex_polar_negation
5theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
6instantiation10, 19  ⊢  
  :
7instantiation20, 11, 12  ⊢  
  : , : , :
8theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
9instantiation13, 28, 14  ⊢  
  : , :
10theorem  ⊢  
 proveit.numbers.addition.elim_zero_left
11instantiation25, 15  ⊢  
  : , : , :
12instantiation16, 17  ⊢  
  :
13theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
14instantiation18, 33, 19  ⊢  
  : , :
15instantiation20, 21, 22  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
17instantiation40, 34, 23  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
19instantiation40, 34, 24  ⊢  
  : , : , :
20axiom  ⊢  
 proveit.logic.equality.equals_transitivity
21instantiation25, 26  ⊢  
  : , : , :
22instantiation27, 28  ⊢  
  :
23instantiation40, 29, 30  ⊢  
  : , : , :
24instantiation40, 38, 31  ⊢  
  : , : , :
25axiom  ⊢  
 proveit.logic.equality.substitution
26instantiation32, 33  ⊢  
  :
27theorem  ⊢  
 proveit.numbers.exponentiation.exp_zero_eq_one
28instantiation40, 34, 35  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
30instantiation40, 36, 37  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
32theorem  ⊢  
 proveit.numbers.multiplication.mult_zero_right
33theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
34theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
35instantiation40, 38, 39  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
37instantiation40, 41, 42  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
39theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
40theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
41theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
42theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements