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.division.prod_of_fracs
2reference23  ⊢  
3reference35  ⊢  
4instantiation57, 31, 8  ⊢  
  : , : , :
5instantiation57, 31, 9  ⊢  
  : , : , :
6instantiation10, 35  ⊢  
  :
7instantiation11, 12, 13  ⊢  
  : , : , :
8instantiation57, 39, 14  ⊢  
  : , : , :
9instantiation57, 39, 15  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.division.frac_one_denom
11axiom  ⊢  
 proveit.logic.equality.equals_transitivity
12instantiation16, 59, 17, 18, 19, 20  ⊢  
  : , : , : , :
13instantiation21, 22, 23, 24*, 25*  ⊢  
  : , : , :
14instantiation57, 45, 26  ⊢  
  : , : , :
15instantiation57, 45, 27  ⊢  
  : , : , :
16axiom  ⊢  
 proveit.core_expr_types.operations.operands_substitution
17instantiation28  ⊢  
  : , :
18instantiation28  ⊢  
  : , :
19instantiation29, 35  ⊢  
  :
20instantiation34, 30  ⊢  
  :
21theorem  ⊢  
 proveit.numbers.division.frac_cancel_left
22instantiation57, 31, 32  ⊢  
  : , : , :
23instantiation57, 42, 33  ⊢  
  : , : , :
24instantiation34, 35  ⊢  
  :
25theorem  ⊢  
 proveit.numbers.numerals.decimals.mult_2_2
26instantiation57, 51, 36  ⊢  
  : , : , :
27instantiation57, 51, 37  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
29theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
30instantiation57, 42, 38  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
32instantiation57, 39, 40  ⊢  
  : , : , :
33instantiation57, 48, 41  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
35instantiation57, 42, 43  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat4
37theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
38instantiation57, 48, 44  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
40instantiation57, 45, 46  ⊢  
  : , : , :
41instantiation57, 54, 47  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
43instantiation57, 48, 49  ⊢  
  : , : , :
44instantiation57, 54, 50  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
46instantiation57, 51, 52  ⊢  
  : , : , :
47instantiation57, 58, 53  ⊢  
  : , : , :
48theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
49instantiation57, 54, 55  ⊢  
  : , : , :
50instantiation57, 58, 56  ⊢  
  : , : , :
51theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
52theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
53theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
54theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
55instantiation57, 58, 59  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
57theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
59theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements