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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, , ,  ⊢  
  : , : , :
1reference28  ⊢  
2instantiation28, 4, 5, , ,  ⊢  
  : , : , :
3instantiation6, 35, 34, 33, 37, 7, 8, 9, 10, , ,  ⊢  
  : , : , : , : , : , :
4instantiation11, 14, 17, 51, ,  ⊢  
  : , : , :
5instantiation12, 13, ,  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.multiplication.disassociation
7instantiation43  ⊢  
  : , :
8instantiation16, 14, 40,  ⊢  
  : , :
9instantiation16, 14, 15, ,  ⊢  
  : , :
10instantiation16, 17, 41,  ⊢  
  : , :
11theorem  ⊢  
 proveit.numbers.exponentiation.pos_power_of_product
12axiom  ⊢  
 proveit.logic.equality.substitution
13instantiation18, 25, 46, 49, 21, 19, ,  ⊢  
  : , : , : , :
14instantiation54, 45, 20  ⊢  
  : , : , :
15instantiation54, 45, 21,  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
17instantiation54, 45, 22  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.exponentiation.exp_factored_real
19instantiation23, 24,  ⊢  
  : , :
20instantiation54, 50, 25  ⊢  
  : , : , :
21instantiation26, 46, 44,  ⊢  
  : , :
22instantiation54, 52, 27  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.logic.equality.equals_reversal
24instantiation28, 29, 30,  ⊢  
  : , : , :
25assumption  ⊢  
26theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
27instantiation54, 55, 31  ⊢  
  : , : , :
28axiom  ⊢  
 proveit.logic.equality.equals_transitivity
29instantiation32, 33, 34, 35, 36, 37, 40, 41, 38,  ⊢  
  : , : , : , : , : , :
30instantiation39, 40, 41, 42,  ⊢  
  : , : , :
31assumption  ⊢  
32theorem  ⊢  
 proveit.numbers.addition.disassociation
33theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
34theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
35axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
36instantiation43  ⊢  
  : , :
37theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
38instantiation54, 45, 44  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_13
40instantiation54, 45, 49  ⊢  
  : , : , :
41instantiation54, 45, 46  ⊢  
  : , : , :
42instantiation47  ⊢  
  :
43theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
44instantiation48, 49  ⊢  
  :
45theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
46instantiation54, 50, 51  ⊢  
  : , : , :
47axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
48theorem  ⊢  
 proveit.numbers.negation.real_closure
49instantiation54, 52, 53  ⊢  
  : , : , :
50theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
51assumption  ⊢  
52theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
53instantiation54, 55, 56  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
55theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
56assumption  ⊢