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  ⊢  
  : , : , :
1theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_12
2instantiation37, 6, 5  ⊢  
  : , : , :
3instantiation37, 6, 7  ⊢  
  : , : , :
4instantiation8  ⊢  
  :
5instantiation9, 10, 11, 12  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
7instantiation13, 14, 19  ⊢  
  : , :
8axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
9theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_cc__is__real
10instantiation15, 16  ⊢  
  :
11theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
12assumption  ⊢  
13theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
14instantiation37, 26, 17  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.negation.real_closure
16instantiation18, 19, 20, 21  ⊢  
  : , :
17instantiation37, 22, 23  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.division.div_real_closure
19instantiation37, 24, 25  ⊢  
  : , : , :
20instantiation37, 26, 27  ⊢  
  : , : , :
21instantiation28, 36  ⊢  
  :
22theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
23instantiation29, 30, 31  ⊢  
  : , :
24theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
25theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
26theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
27instantiation37, 32, 33  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
29theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
30instantiation37, 35, 34  ⊢  
  : , : , :
31instantiation37, 35, 36  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
33instantiation37, 38, 39  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
35theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
36theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
37theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
38theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
39theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2