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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  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_23
2reference26  ⊢  
3instantiation5, 6, 7  ⊢  
  : , : , :
4instantiation8  ⊢  
  :
5theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
6instantiation15, 9, 14  ⊢  
  : , :
7instantiation10, 11, 48, 43, 12, 13, 36, 16, 14  ⊢  
  : , : , : , : , : , :
8axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
9instantiation15, 36, 16  ⊢  
  : , :
10theorem  ⊢  
 proveit.numbers.multiplication.disassociation
11axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
12theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
13instantiation17  ⊢  
  : , :
14instantiation46, 38, 18  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
16instantiation19, 26, 20, 21  ⊢  
  : , :
17theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
18instantiation22, 23, 24  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.division.div_complex_closure
20instantiation25, 36, 26  ⊢  
  : , :
21instantiation27, 28, 29  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
23instantiation30, 31  ⊢  
  : , :
24theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
25theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
26instantiation46, 38, 32  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.logic.equality.sub_left_side_into
28instantiation33, 34  ⊢  
  :
29instantiation35, 36  ⊢  
  :
30theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
31theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
32instantiation46, 41, 37  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
34theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
35theorem  ⊢  
 proveit.numbers.exponentiation.complex_x_to_first_power_is_x
36instantiation46, 38, 39  ⊢  
  : , : , :
37instantiation46, 44, 40  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
39instantiation46, 41, 42  ⊢  
  : , : , :
40instantiation46, 47, 43  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
42instantiation46, 44, 45  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
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