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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
2instantiation7, 5  ⊢  
  : , : , :
3instantiation7, 6  ⊢  
  : , : , :
4instantiation7, 8  ⊢  
  : , : , :
5instantiation11, 9  ⊢  
  :
6instantiation11, 10  ⊢  
  :
7axiom  ⊢  
 proveit.logic.equality.substitution
8instantiation11, 12  ⊢  
  :
9instantiation15, 13  ⊢  
  : , :
10instantiation15, 14  ⊢  
  : , :
11axiom  ⊢  
 proveit.logic.booleans.negation.negation_elim
12instantiation15, 16  ⊢  
  : , :
13instantiation17, 18  ⊢  
  : , :
14instantiation23, 48, 19, 20  ⊢  
  : , :
15theorem  ⊢  
 proveit.logic.equality.unfold_not_equals
16instantiation23, 48, 21, 22  ⊢  
  : , :
17theorem  ⊢  
 proveit.logic.equality.not_equals_symmetry
18instantiation23, 24, 48, 25  ⊢  
  : , :
19theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
20theorem  ⊢  
 proveit.numbers.numerals.decimals.less_2_3
21theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
22instantiation26, 41, 27, 28, 29*, 30*  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.ordering.less_is_not_eq_nat
24theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
25theorem  ⊢  
 proveit.numbers.numerals.decimals.less_1_2
26theorem  ⊢  
 proveit.numbers.addition.strong_bound_via_left_term_bound
27theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
28instantiation31, 32  ⊢  
  :
29instantiation33, 34, 35  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.numerals.decimals.add_2_2
31theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
32theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
33theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
34instantiation36, 38  ⊢  
  :
35instantiation37, 38, 39  ⊢  
  : , :
36theorem  ⊢  
 proveit.numbers.addition.elim_zero_right
37theorem  ⊢  
 proveit.numbers.addition.commutation
38instantiation46, 40, 41  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
40theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
41instantiation46, 42, 43  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
43instantiation46, 44, 45  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
45instantiation46, 47, 48  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
47theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
48theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements