logo

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, 4, 5, 6, 7,  ⊢  
  : , : , : , : , : , : , :
1theorem  ⊢  
 proveit.numbers.addition.leftward_commutation
2reference29  ⊢  
3axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
4theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
5instantiation37, 13, 8,  ⊢  
  : , : , :
6instantiation9, 10  ⊢  
  :
7instantiation37, 13, 11  ⊢  
  : , : , :
8instantiation37, 18, 12,  ⊢  
  : , : , :
9theorem  ⊢  
 proveit.numbers.negation.complex_closure
10instantiation37, 13, 14  ⊢  
  : , : , :
11instantiation15, 16, 39  ⊢  
  : , : , :
12instantiation37, 24, 17,  ⊢  
  : , : , :
13theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
14instantiation37, 18, 19  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
16instantiation20, 21  ⊢  
  : , :
17instantiation37, 22, 23,  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
19instantiation37, 24, 25  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
21theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
22instantiation26, 27, 28  ⊢  
  : , :
23assumption  ⊢  
24theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
25instantiation37, 35, 29  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
27instantiation30, 31, 32  ⊢  
  : , :
28theorem  ⊢  
 proveit.numbers.number_sets.integers.zero_is_int
29theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
30theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
31instantiation33, 34  ⊢  
  :
32instantiation37, 35, 36  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.negation.int_closure
34instantiation37, 38, 39  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
36theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
37theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
38theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
39assumption  ⊢