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  ⊢  
  : , : , :
1reference14  ⊢  
2instantiation22, 23, 4, 5, 6, 7  ⊢  
  : , : , : , :
3instantiation8, 9, 10, 11, 12*, 13*  ⊢  
  : , : , :
4instantiation33  ⊢  
  : , :
5instantiation33  ⊢  
  : , :
6instantiation14, 15, 16  ⊢  
  : , : , :
7theorem  ⊢  
 proveit.numbers.numerals.decimals.mult_4_4
8theorem  ⊢  
 proveit.numbers.division.frac_cancel_left
9instantiation54, 18, 17  ⊢  
  : , : , :
10instantiation54, 18, 19  ⊢  
  : , : , :
11instantiation54, 42, 20  ⊢  
  : , : , :
12instantiation35, 21  ⊢  
  :
13theorem  ⊢  
 proveit.numbers.numerals.decimals.mult_8_2
14axiom  ⊢  
 proveit.logic.equality.equals_transitivity
15instantiation22, 23, 24, 25, 26, 27  ⊢  
  : , : , : , :
16theorem  ⊢  
 proveit.numbers.numerals.decimals.add_4_4
17instantiation54, 29, 28  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
19instantiation54, 29, 30  ⊢  
  : , : , :
20instantiation54, 49, 31  ⊢  
  : , : , :
21instantiation54, 42, 32  ⊢  
  : , : , :
22axiom  ⊢  
 proveit.core_expr_types.operations.operands_substitution
23theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
24instantiation33  ⊢  
  : , :
25instantiation33  ⊢  
  : , :
26instantiation34, 36  ⊢  
  :
27instantiation35, 36  ⊢  
  :
28instantiation54, 38, 37  ⊢  
  : , : , :
29theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
30instantiation54, 38, 39  ⊢  
  : , : , :
31instantiation54, 52, 40  ⊢  
  : , : , :
32instantiation54, 49, 41  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
34theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
35theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
36instantiation54, 42, 43  ⊢  
  : , : , :
37instantiation54, 45, 44  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
39instantiation54, 45, 46  ⊢  
  : , : , :
40instantiation54, 55, 47  ⊢  
  : , : , :
41instantiation54, 52, 48  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
43instantiation54, 49, 50  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat8
45theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
46theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
47theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
48instantiation54, 55, 51  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
50instantiation54, 52, 53  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.numerals.decimals.nat8
52theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
53instantiation54, 55, 56  ⊢  
  : , : , :
54theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
55theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
56theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
*equality replacement requirements