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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.logic.equality.four_chain_transitivity
2instantiation5, 35, 48, 6*  ⊢  
  : , : , : , :
3instantiation7  ⊢  
  :
4instantiation8, 9  ⊢  
  : , :
5theorem  ⊢  
 proveit.numbers.addition.rational_pair_addition
6instantiation22, 10, 11  ⊢  
  : , : , :
7axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
8theorem  ⊢  
 proveit.logic.equality.equals_reversal
9instantiation12, 13  ⊢  
  :
10instantiation29, 51, 14, 15, 16, 17  ⊢  
  : , : , : , :
11instantiation18, 19, 20  ⊢  
  :
12theorem  ⊢  
 proveit.numbers.addition.elim_zero_left
13instantiation49, 42, 21  ⊢  
  : , : , :
14instantiation36  ⊢  
  : , :
15instantiation36  ⊢  
  : , :
16instantiation22, 23, 24  ⊢  
  : , : , :
17theorem  ⊢  
 proveit.numbers.numerals.decimals.mult_2_2
18theorem  ⊢  
 proveit.numbers.division.frac_cancel_complete
19instantiation49, 42, 25  ⊢  
  : , : , :
20instantiation26, 27  ⊢  
  :
21instantiation49, 45, 28  ⊢  
  : , : , :
22axiom  ⊢  
 proveit.logic.equality.equals_transitivity
23instantiation29, 51, 30, 31, 32, 33  ⊢  
  : , : , : , :
24theorem  ⊢  
 proveit.numbers.numerals.decimals.add_2_2
25instantiation49, 45, 34  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
27theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat4
28instantiation49, 47, 35  ⊢  
  : , : , :
29axiom  ⊢  
 proveit.core_expr_types.operations.operands_substitution
30instantiation36  ⊢  
  : , :
31instantiation36  ⊢  
  : , :
32instantiation37, 39  ⊢  
  :
33instantiation38, 39  ⊢  
  :
34instantiation49, 47, 40  ⊢  
  : , : , :
35instantiation49, 50, 41  ⊢  
  : , : , :
36theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
37theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
38theorem  ⊢  
 proveit.numbers.multiplication.elim_one_right
39instantiation49, 42, 43  ⊢  
  : , : , :
40instantiation49, 50, 44  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
42theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
43instantiation49, 45, 46  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
45theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
46instantiation49, 47, 48  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
48instantiation49, 50, 51  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
51theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements