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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, 7*,  ⊢  
  : , : , : , :
1theorem  ⊢  
 proveit.numbers.exponentiation.exp_factored_real
2reference30  ⊢  
3reference35  ⊢  
4reference38  ⊢  
5instantiation45, 40, 8  ⊢  
  : , : , :
6instantiation9, 10  ⊢  
  : , :
7instantiation11, 12  ⊢  
  :
8instantiation45, 43, 13  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.logic.equality.equals_reversal
10instantiation14, 15, 16  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
12instantiation45, 37, 17  ⊢  
  : , : , :
13instantiation18, 42, 19  ⊢  
  : , :
14axiom  ⊢  
 proveit.logic.equality.equals_transitivity
15instantiation20, 47, 21, 22, 23, 24, 34, 27, 25  ⊢  
  : , : , : , : , : , :
16instantiation26, 34, 27, 28  ⊢  
  : , : , :
17instantiation45, 29, 30  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
19instantiation31, 44  ⊢  
  :
20theorem  ⊢  
 proveit.numbers.addition.disassociation
21theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
22axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
23instantiation32  ⊢  
  : , :
24theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
25instantiation33, 34  ⊢  
  :
26theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_13
27instantiation45, 37, 35  ⊢  
  : , : , :
28instantiation36  ⊢  
  :
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
30assumption  ⊢  
31theorem  ⊢  
 proveit.numbers.negation.int_closure
32theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
33theorem  ⊢  
 proveit.numbers.negation.complex_closure
34instantiation45, 37, 38  ⊢  
  : , : , :
35instantiation45, 40, 39  ⊢  
  : , : , :
36axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
37theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
38instantiation45, 40, 41  ⊢  
  : , : , :
39instantiation45, 43, 42  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
41instantiation45, 43, 44  ⊢  
  : , : , :
42assumption  ⊢  
43theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
44instantiation45, 46, 47  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
46theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
47theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements