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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,  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
2instantiation4, 5, 6, 7, 8*  ⊢  
  : , : , : , :
3assumption  ⊢  
4axiom  ⊢  
 proveit.numbers.summation.sum_split_last
5theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
6instantiation9, 10, 42  ⊢  
  : , :
7instantiation11, 12  ⊢  
  :
8instantiation13, 14, 15  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
10instantiation43, 44, 36  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
12instantiation16, 45, 19, 21, 36, 17  ⊢  
  : , : , : , : , :
13axiom  ⊢  
 proveit.logic.equality.equals_transitivity
14instantiation18, 19, 20, 45, 21, 22, 25, 29, 23  ⊢  
  : , : , : , : , : , :
15instantiation24, 29, 25, 26  ⊢  
  : , : , :
16theorem  ⊢  
 proveit.numbers.addition.add_nat_pos_from_nonneg
17theorem  ⊢  
 proveit.numbers.numerals.decimals.less_0_1
18theorem  ⊢  
 proveit.numbers.addition.disassociation
19axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
20theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
21theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
22instantiation27  ⊢  
  : , :
23instantiation28, 29  ⊢  
  :
24theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_23
25instantiation43, 32, 30  ⊢  
  : , : , :
26instantiation31  ⊢  
  :
27theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
28theorem  ⊢  
 proveit.numbers.negation.complex_closure
29instantiation43, 32, 33  ⊢  
  : , : , :
30instantiation34, 35, 36  ⊢  
  : , : , :
31axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
32theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
33instantiation43, 37, 38  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
35instantiation39, 40  ⊢  
  : , :
36assumption  ⊢  
37theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
38instantiation43, 41, 42  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_within_real
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