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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  ⊢  
  : , : , :
1reference4  ⊢  
2instantiation4, 3  ⊢  
  : , : , :
3instantiation4, 5  ⊢  
  : , : , :
4axiom  ⊢  
 proveit.logic.equality.substitution
5instantiation6, 7, 8, 9*  ⊢  
  : , :
6theorem  ⊢  
 proveit.numbers.negation.distribute_neg_through_binary_sum
7instantiation30, 17, 10  ⊢  
  : , : , :
8instantiation30, 17, 11  ⊢  
  : , : , :
9instantiation12, 13  ⊢  
  :
10instantiation30, 15, 14  ⊢  
  : , : , :
11instantiation30, 15, 16  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.negation.double_negation
13instantiation30, 17, 18  ⊢  
  : , : , :
14instantiation30, 20, 19  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
16instantiation30, 20, 21  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
18instantiation22, 23, 32  ⊢  
  : , : , :
19instantiation24, 25  ⊢  
  :
20theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
21instantiation30, 26, 27  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
23instantiation28, 29  ⊢  
  : , :
24theorem  ⊢  
 proveit.numbers.negation.int_closure
25instantiation30, 31, 32  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
27theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
28theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
30theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
31theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
32assumption  ⊢  
*equality replacement requirements