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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  ⊢  
  :
1theorem  ⊢  
 proveit.numbers.negation.nat_closure
2instantiation3, 4, 5  ⊢  
  :
3theorem  ⊢  
 proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
4instantiation6, 30, 28  ⊢  
  : , :
5instantiation7, 19, 18, 21, 8, 9*, 10*  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
7theorem  ⊢  
 proveit.numbers.addition.weak_bound_via_left_term_bound
8instantiation11, 39  ⊢  
  :
9instantiation12, 13, 14  ⊢  
  : , :
10instantiation15, 16, 17  ⊢  
  : , :
11theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
12theorem  ⊢  
 proveit.numbers.addition.commutation
13instantiation37, 20, 18  ⊢  
  : , : , :
14instantiation37, 20, 19  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_basic
16instantiation37, 20, 21  ⊢  
  : , : , :
17instantiation22  ⊢  
  :
18instantiation37, 24, 23  ⊢  
  : , : , :
19instantiation37, 24, 25  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
21instantiation26, 27, 39  ⊢  
  : , : , :
22axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
23instantiation37, 29, 28  ⊢  
  : , : , :
24theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
25instantiation37, 29, 30  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
27instantiation31, 32  ⊢  
  : , :
28instantiation37, 33, 34  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
30instantiation35, 36  ⊢  
  :
31theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
32theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
33theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
34theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
35theorem  ⊢  
 proveit.numbers.negation.int_closure
36instantiation37, 38, 39  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
38theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
39assumption  ⊢  
*equality replacement requirements