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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, , ,  ⊢  
  : , : , :
1reference32  ⊢  
2instantiation32, 4, 5, , ,  ⊢  
  : , : , :
3instantiation6, 37, 38, 39, 7, 41, 12, 13, 14, , ,  ⊢  
  : , : , : , : , : , :
4instantiation32, 8, 9, , ,  ⊢  
  : , : , :
5instantiation10, 39, 38, 37, 41, 11, 12, 13, 14, , ,  ⊢  
  : , : , : , : , : , :
6theorem  ⊢  
 proveit.numbers.multiplication.association
7instantiation47  ⊢  
  : , :
8instantiation15, 18, 21, 55, ,  ⊢  
  : , : , :
9instantiation16, 17, ,  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.multiplication.disassociation
11instantiation47  ⊢  
  : , :
12instantiation20, 18, 44,  ⊢  
  : , :
13instantiation20, 18, 19, ,  ⊢  
  : , :
14instantiation20, 21, 45,  ⊢  
  : , :
15theorem  ⊢  
 proveit.numbers.exponentiation.pos_power_of_product
16axiom  ⊢  
 proveit.logic.equality.substitution
17instantiation22, 29, 50, 53, 25, 23, ,  ⊢  
  : , : , : , :
18instantiation58, 49, 24  ⊢  
  : , : , :
19instantiation58, 49, 25,  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.exponentiation.exp_complex_closure
21instantiation58, 49, 26  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.exponentiation.exp_factored_real
23instantiation27, 28,  ⊢  
  : , :
24instantiation58, 54, 29  ⊢  
  : , : , :
25instantiation30, 50, 48,  ⊢  
  : , :
26instantiation58, 56, 31  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.logic.equality.equals_reversal
28instantiation32, 33, 34,  ⊢  
  : , : , :
29assumption  ⊢  
30theorem  ⊢  
 proveit.numbers.addition.add_real_closure_bin
31instantiation58, 59, 35  ⊢  
  : , : , :
32axiom  ⊢  
 proveit.logic.equality.equals_transitivity
33instantiation36, 37, 38, 39, 40, 41, 44, 45, 42,  ⊢  
  : , : , : , : , : , :
34instantiation43, 44, 45, 46,  ⊢  
  : , : , :
35assumption  ⊢  
36theorem  ⊢  
 proveit.numbers.addition.disassociation
37theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
38theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
39axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
40instantiation47  ⊢  
  : , :
41theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
42instantiation58, 49, 48  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_13
44instantiation58, 49, 53  ⊢  
  : , : , :
45instantiation58, 49, 50  ⊢  
  : , : , :
46instantiation51  ⊢  
  :
47theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
48instantiation52, 53  ⊢  
  :
49theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
50instantiation58, 54, 55  ⊢  
  : , : , :
51axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
52theorem  ⊢  
 proveit.numbers.negation.real_closure
53instantiation58, 56, 57  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
55assumption  ⊢  
56theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
57instantiation58, 59, 60  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
59theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
60assumption  ⊢