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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,  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.substitution
2instantiation3, 28, 33, 36, 4, 5, 6*,  ⊢  
  : , : , : , :
3theorem  ⊢  
 proveit.numbers.exponentiation.exp_factored_real
4instantiation7, 33, 8  ⊢  
  : , :
5instantiation9, 10  ⊢  
  : , :
6instantiation11, 12  ⊢  
  :
7theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
8instantiation43, 39, 13  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.logic.equality.equals_reversal
10instantiation14, 15, 16  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
12instantiation43, 35, 17  ⊢  
  : , : , :
13instantiation43, 41, 18  ⊢  
  : , : , :
14axiom  ⊢  
 proveit.logic.equality.equals_transitivity
15instantiation19, 45, 20, 21, 22, 23, 32, 26, 24  ⊢  
  : , : , : , : , : , :
16instantiation25, 32, 26, 27  ⊢  
  : , : , :
17instantiation43, 37, 28  ⊢  
  : , : , :
18instantiation29, 42  ⊢  
  :
19theorem  ⊢  
 proveit.numbers.addition.disassociation
20theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
21axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
22instantiation30  ⊢  
  : , :
23theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
24instantiation31, 32  ⊢  
  :
25theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_13
26instantiation43, 35, 33  ⊢  
  : , : , :
27instantiation34  ⊢  
  :
28assumption  ⊢  
29theorem  ⊢  
 proveit.numbers.negation.int_closure
30theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
31theorem  ⊢  
 proveit.numbers.negation.complex_closure
32instantiation43, 35, 36  ⊢  
  : , : , :
33instantiation43, 37, 38  ⊢  
  : , : , :
34axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
35theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
36instantiation43, 39, 40  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
38assumption  ⊢  
39theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
40instantiation43, 41, 42  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
42instantiation43, 44, 45  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
45theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements