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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  ⊢  
  : , : , :
3instantiation6, 7, 8  ⊢  
  : , : , :
4theorem  ⊢  
 proveit.core_expr_types.tuples.range_len
5instantiation9, 10, 11, 12, 13, 39  ⊢  
  : , :
6axiom  ⊢  
 proveit.logic.equality.equals_transitivity
7instantiation14, 27  ⊢  
  : , : , :
8instantiation15, 39, 16, 17  ⊢  
  : , : , : , :
9theorem  ⊢  
 proveit.numbers.addition.add_nat_closure
10theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
11instantiation18  ⊢  
  : , : , :
12instantiation37, 19, 30  ⊢  
  : , : , :
13instantiation28, 20, 21  ⊢  
  : , : , :
14axiom  ⊢  
 proveit.logic.equality.substitution
15theorem  ⊢  
 proveit.numbers.addition.elim_zero_any
16instantiation37, 23, 22  ⊢  
  : , : , :
17instantiation37, 23, 24  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
19theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
20instantiation33, 25  ⊢  
  : , :
21instantiation26, 27  ⊢  
  : , :
22instantiation28, 29, 30  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
24instantiation37, 31, 32  ⊢  
  : , : , :
25theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_set_within_nat
26theorem  ⊢  
 proveit.logic.sets.enumeration.fold_singleton
27theorem  ⊢  
 proveit.numbers.negation.negated_zero
28theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
29instantiation33, 34  ⊢  
  : , :
30assumption  ⊢  
31theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
32instantiation37, 35, 36  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
34theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
35theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
36instantiation37, 38, 39  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
38theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
39theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1