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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, , , ,  ⊢  
  : , : , :
1reference8  ⊢  
2instantiation49, 43, 4, , , ,  ⊢  
  : , :
3instantiation5, 6, 7, , , ,  ⊢  
  : , : , :
4instantiation8, 9, 10, ,  ⊢  
  : , : , :
5axiom  ⊢  
 proveit.logic.equality.equals_transitivity
6instantiation18, 21, 12, 19, 14, 22, 11, 24, 25, 26, , , ,  ⊢  
  : , : , : , : , : , :
7instantiation18, 19, 20, 12, 22, 13, 14, 15, 16, 24, 25, 26, , , ,  ⊢  
  : , : , : , : , : , :
8theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
9instantiation49, 17, 48, ,  ⊢  
  : , :
10instantiation18, 19, 20, 21, 22, 23, 24, 25, 26, ,  ⊢  
  : , : , : , : , : , :
11instantiation46, 34, 27,  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
13instantiation31  ⊢  
  : , :
14instantiation28  ⊢  
  : , : , :
15instantiation46, 34, 29  ⊢  
  : , : , :
16instantiation46, 34, 30  ⊢  
  : , : , :
17instantiation49, 44, 45,  ⊢  
  : , :
18theorem  ⊢  
 proveit.numbers.multiplication.disassociation
19axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
20theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
21theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
22theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
23instantiation31  ⊢  
  : , :
24instantiation46, 34, 32  ⊢  
  : , : , :
25instantiation46, 34, 33  ⊢  
  : , : , :
26instantiation46, 34, 35  ⊢  
  : , : , :
27instantiation46, 41, 36,  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
29instantiation46, 41, 37  ⊢  
  : , : , :
30instantiation46, 41, 38  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
32instantiation46, 41, 39  ⊢  
  : , : , :
33instantiation46, 41, 40  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
35instantiation46, 41, 42  ⊢  
  : , : , :
36instantiation46, 47, 43,  ⊢  
  : , : , :
37instantiation46, 47, 50  ⊢  
  : , : , :
38instantiation46, 47, 51  ⊢  
  : , : , :
39instantiation46, 47, 44  ⊢  
  : , : , :
40instantiation46, 47, 45  ⊢  
  : , : , :
41theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
42instantiation46, 47, 48  ⊢  
  : , : , :
43instantiation49, 50, 51,  ⊢  
  : , :
44assumption  ⊢  
45assumption  ⊢  
46theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
47theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
48assumption  ⊢  
49theorem  ⊢  
 proveit.numbers.multiplication.mult_int_closure_bin
50assumption  ⊢  
51assumption  ⊢