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  ⊢  
  : , : , :
1reference6  ⊢  
2instantiation3, 4, 5  ⊢  
  : , : , :
3axiom  ⊢  
 proveit.logic.equality.equals_transitivity
4instantiation6, 7  ⊢  
  : , : , :
5instantiation8, 9  ⊢  
  : , :
6axiom  ⊢  
 proveit.logic.equality.substitution
7instantiation10, 13, 12  ⊢  
  : , :
8theorem  ⊢  
 proveit.logic.equality.equals_reversal
9instantiation11, 12, 13, 14, 15  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.multiplication.commutation
11theorem  ⊢  
 proveit.numbers.division.mult_frac_left
12instantiation38, 18, 16  ⊢  
  : , : , :
13instantiation38, 18, 17  ⊢  
  : , : , :
14instantiation38, 18, 19  ⊢  
  : , : , :
15instantiation20, 21  ⊢  
  :
16instantiation38, 25, 22  ⊢  
  : , : , :
17instantiation23, 24, 37  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
19instantiation38, 25, 26  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
21theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
22instantiation38, 30, 27  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
24instantiation28, 29  ⊢  
  : , :
25theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
26instantiation38, 30, 31  ⊢  
  : , : , :
27instantiation32, 33, 34  ⊢  
  : , :
28theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
30theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
31instantiation38, 39, 35  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
33instantiation38, 36, 37  ⊢  
  : , : , :
34instantiation38, 39, 40  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
36theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
37assumption  ⊢  
38theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
39theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
40theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1