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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.exponentiation.real_power_of_product
2instantiation7, 11, 12  ⊢  
  : , :
3instantiation54, 45, 8,  ⊢  
  : , : , :
4instantiation54, 48, 9  ⊢  
  : , : , :
5instantiation10, 11, 12, 13  ⊢  
  : , :
6assumption  ⊢  
7theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
8instantiation14, 15, 16,  ⊢  
  : , :
9instantiation54, 52, 17  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.exponentiation.exp_not_eq_zero
11instantiation54, 45, 18  ⊢  
  : , : , :
12instantiation19, 20, 21  ⊢  
  : , : , :
13instantiation22, 23  ⊢  
  :
14theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
15assumption  ⊢  
16assumption  ⊢  
17assumption  ⊢  
18instantiation54, 50, 29  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
20instantiation39, 31, 24  ⊢  
  : , :
21instantiation25, 26, 27  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
23instantiation54, 28, 29  ⊢  
  : , : , :
24instantiation39, 37, 38  ⊢  
  : , :
25axiom  ⊢  
 proveit.logic.equality.equals_transitivity
26instantiation32, 30, 56, 33, 36, 34, 31, 37, 38  ⊢  
  : , : , : , : , : , :
27instantiation32, 33, 56, 34, 35, 36, 40, 41, 37, 38  ⊢  
  : , : , : , : , : , :
28theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
30theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
31instantiation39, 40, 41  ⊢  
  : , :
32theorem  ⊢  
 proveit.numbers.multiplication.disassociation
33axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
34theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
35instantiation42  ⊢  
  : , :
36instantiation42  ⊢  
  : , :
37theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
38instantiation54, 45, 43  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
40instantiation54, 45, 44  ⊢  
  : , : , :
41instantiation54, 45, 46  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
43instantiation54, 50, 47  ⊢  
  : , : , :
44instantiation54, 48, 49  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
46instantiation54, 50, 51  ⊢  
  : , : , :
47assumption  ⊢  
48theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
49instantiation54, 52, 53  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
51theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
52theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
53instantiation54, 55, 56  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
55theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
56theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2