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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,  ⊢  
  : , : , :
1reference33  ⊢  
2instantiation4, 5, 6, 7, 8, 9,  ⊢  
  : , : , : , :
3instantiation10, 11  ⊢  
  :
4axiom  ⊢  
 proveit.core_expr_types.operations.operands_substitution
5theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
6instantiation12  ⊢  
  : , :
7instantiation12  ⊢  
  : , :
8instantiation13, 14, 15*  ⊢  
  : , :
9instantiation33, 16, 17,  ⊢  
  : , : , :
10axiom  ⊢  
 proveit.logic.booleans.eq_true_intro
11instantiation18  ⊢  
  :
12theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13axiom  ⊢  
 proveit.numbers.summation.sum_single
14theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
15instantiation19, 39  ⊢  
  :
16instantiation36, 20  ⊢  
  : , : , :
17instantiation21, 22, 23,  ⊢  
  :
18axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
19theorem  ⊢  
 proveit.numbers.exponentiation.exp_zero_eq_one
20instantiation36, 24  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.division.frac_cancel_complete
22instantiation25, 41, 26  ⊢  
  : , :
23instantiation27, 28  ⊢  
  : , :
24instantiation36, 29  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.addition.add_complex_closure_bin
26instantiation30, 39  ⊢  
  :
27theorem  ⊢  
 proveit.numbers.addition.subtraction.nonzero_difference_if_different
28instantiation31, 32  ⊢  
  : , :
29instantiation33, 34, 35  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.negation.complex_closure
31theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
32assumption  ⊢  
33axiom  ⊢  
 proveit.logic.equality.equals_transitivity
34instantiation36, 37  ⊢  
  : , : , :
35instantiation38, 39  ⊢  
  :
36axiom  ⊢  
 proveit.logic.equality.substitution
37instantiation40, 41  ⊢  
  :
38theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
39assumption  ⊢  
40theorem  ⊢  
 proveit.numbers.addition.elim_zero_left
41instantiation48, 42, 43  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
43instantiation48, 44, 45  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
45instantiation48, 46, 47  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
47instantiation48, 49, 50  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
49theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
50theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements