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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,  ⊢  
  : , :
3instantiation7, 8  ⊢  
  :
4instantiation46, 36, 9  ⊢  
  : , : , :
5instantiation10, 11, 12  ⊢  
  : , : , :
6instantiation13, 14  ⊢  
  :
7theorem  ⊢  
 proveit.numbers.exponentiation.int_exp_of_exp
8assumption  ⊢  
9instantiation46, 41, 20  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
11instantiation30, 22, 15  ⊢  
  : , :
12instantiation16, 17, 18  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
14instantiation46, 19, 20  ⊢  
  : , : , :
15instantiation30, 28, 29  ⊢  
  : , :
16axiom  ⊢  
 proveit.logic.equality.equals_transitivity
17instantiation23, 21, 48, 24, 27, 25, 22, 28, 29  ⊢  
  : , : , : , : , : , :
18instantiation23, 24, 48, 25, 26, 27, 31, 32, 28, 29  ⊢  
  : , : , : , : , : , :
19theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
20theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.e_is_real_pos
21theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
22instantiation30, 31, 32  ⊢  
  : , :
23theorem  ⊢  
 proveit.numbers.multiplication.disassociation
24axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
25theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
26instantiation33  ⊢  
  : , :
27instantiation33  ⊢  
  : , :
28theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
29instantiation46, 36, 34  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
31instantiation46, 36, 35  ⊢  
  : , : , :
32instantiation46, 36, 37  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
34instantiation46, 39, 38  ⊢  
  : , : , :
35instantiation46, 39, 40  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
37instantiation46, 41, 42  ⊢  
  : , : , :
38instantiation46, 44, 43  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
40instantiation46, 44, 45  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
42theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
43assumption  ⊢  
44theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
45instantiation46, 47, 48  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
47theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
48theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2