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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, 4, 5, 6, 7, 8, , , ,  ⊢  
  : , : , :
3theorem  ⊢  
 proveit.numbers.exponentiation.real_power_of_product
4instantiation9, 13, 14  ⊢  
  : , :
5instantiation56, 47, 10,  ⊢  
  : , : , :
6instantiation56, 50, 11  ⊢  
  : , : , :
7instantiation12, 13, 14, 15  ⊢  
  : , :
8assumption  ⊢  
9theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
10instantiation16, 17, 18,  ⊢  
  : , :
11instantiation56, 54, 19  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.exponentiation.exp_not_eq_zero
13instantiation56, 47, 20  ⊢  
  : , : , :
14instantiation21, 22, 23  ⊢  
  : , : , :
15instantiation24, 25  ⊢  
  :
16theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
17assumption  ⊢  
18assumption  ⊢  
19assumption  ⊢  
20instantiation56, 52, 31  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
22instantiation41, 33, 26  ⊢  
  : , :
23instantiation27, 28, 29  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
25instantiation56, 30, 31  ⊢  
  : , : , :
26instantiation41, 39, 40  ⊢  
  : , :
27axiom  ⊢  
 proveit.logic.equality.equals_transitivity
28instantiation34, 32, 58, 35, 38, 36, 33, 39, 40  ⊢  
  : , : , : , : , : , :
29instantiation34, 35, 58, 36, 37, 38, 42, 43, 39, 40  ⊢  
  : , : , : , : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
31theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
32theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
33instantiation41, 42, 43  ⊢  
  : , :
34theorem  ⊢  
 proveit.numbers.multiplication.disassociation
35axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
36theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
37instantiation44  ⊢  
  : , :
38instantiation44  ⊢  
  : , :
39theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
40instantiation56, 47, 45  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
42instantiation56, 47, 46  ⊢  
  : , : , :
43instantiation56, 47, 48  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
45instantiation56, 52, 49  ⊢  
  : , : , :
46instantiation56, 50, 51  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
48instantiation56, 52, 53  ⊢  
  : , : , :
49assumption  ⊢  
50theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
51instantiation56, 54, 55  ⊢  
  : , : , :
52theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
53theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
54theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
55instantiation56, 57, 58  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
57theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
58theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2