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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, , , ,  ⊢  
  : , : , :
1reference9  ⊢  
2instantiation3, 4, 5, 47, 46, 37, 6*, , , ,  ⊢  
  : , : , :
3axiom  ⊢  
 proveit.numbers.ordering.min_def_multi
4theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
5instantiation39  ⊢  
  : , :
6instantiation23, 7, 8, , , ,  ⊢  
  : , : , :
7instantiation9, 10, ,  ⊢  
  : , : , :
8instantiation17, 46, 37, 11*, ,  ⊢  
  : , :
9axiom  ⊢  
 proveit.logic.equality.substitution
10instantiation23, 12, 13, ,  ⊢  
  : , : , :
11instantiation23, 14, 15, ,  ⊢  
  : , : , :
12instantiation16, 47, 46,  ⊢  
  : , :
13instantiation17, 46, 47, 18*, ,  ⊢  
  : , :
14instantiation27, 28, 19, 20, 21, 22, ,  ⊢  
  : , : , : , :
15instantiation33, 34, 35, 36  ⊢  
  : , : , : , : , :
16theorem  ⊢  
 proveit.numbers.ordering.min_bin_args_commute
17axiom  ⊢  
 proveit.numbers.ordering.min_def_bin
18instantiation23, 24, 25, ,  ⊢  
  : , : , :
19instantiation39  ⊢  
  : , :
20instantiation39  ⊢  
  : , :
21instantiation40, 38  ⊢  
  : , :
22instantiation41, 26, ,  ⊢  
  : , :
23axiom  ⊢  
 proveit.logic.equality.equals_transitivity
24instantiation27, 28, 29, 30, 31, 32, ,  ⊢  
  : , : , : , :
25instantiation33, 34, 35, 36  ⊢  
  : , : , : , : , :
26instantiation45, 46, 37, 38, ,  ⊢  
  : , :
27axiom  ⊢  
 proveit.core_expr_types.operations.operands_substitution
28theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
29instantiation39  ⊢  
  : , :
30instantiation39  ⊢  
  : , :
31instantiation40, 48  ⊢  
  : , :
32instantiation41, 42, ,  ⊢  
  : , :
33axiom  ⊢  
 proveit.core_expr_types.conditionals.true_case_reduction
34axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
35theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
36theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
37assumption  ⊢  
38instantiation43, 44  ⊢  
  : , :
39theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
40theorem  ⊢  
 proveit.core_expr_types.conditionals.satisfied_condition_reduction
41theorem  ⊢  
 proveit.core_expr_types.conditionals.dissatisfied_condition_reduction
42instantiation45, 46, 47, 48, ,  ⊢  
  : , :
43theorem  ⊢  
 proveit.numbers.ordering.relax_less
44assumption  ⊢  
45theorem  ⊢  
 proveit.numbers.ordering.not_less_from_less_eq
46assumption  ⊢  
47assumption  ⊢  
48assumption  ⊢  
*equality replacement requirements