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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, 5, 6, 7, 8, 9, 10, 11*, ,  ⊢  
  : , : , : , : , : , :
1reference27  ⊢  
2reference51  ⊢  
3reference24  ⊢  
4instantiation38  ⊢  
  : , :
5instantiation35  ⊢  
  : , : , :
6instantiation38  ⊢  
  : , :
7instantiation12, 13, 14  ⊢  
  : , :
8instantiation54, 45, 15  ⊢  
  : , : , :
9reference37  ⊢  
10instantiation54, 45, 16  ⊢  
  : , : , :
11instantiation17, 18, 19*  ⊢  
  : , :
12theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
13instantiation54, 45, 20  ⊢  
  : , : , :
14instantiation54, 45, 21  ⊢  
  : , : , :
15instantiation54, 47, 22  ⊢  
  : , : , :
16assumption  ⊢  
17theorem  ⊢  
 proveit.logic.equality.equals_reversal
18instantiation23, 28, 24, 56, 29, 25, 31, 37, 26*  ⊢  
  : , : , : , : , : , :
19instantiation27, 28, 51, 56, 29, 30, 31, 32*  ⊢  
  : , : , : , : , : , :
20instantiation54, 47, 33  ⊢  
  : , : , :
21assumption  ⊢  
22instantiation54, 52, 34  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.multiplication.distribute_through_sum
24theorem  ⊢  
 proveit.numbers.numerals.decimals.nat3
25instantiation35  ⊢  
  : , : , :
26instantiation36, 37  ⊢  
  :
27theorem  ⊢  
 proveit.numbers.addition.association
28axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
29theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
30instantiation38  ⊢  
  : , :
31instantiation54, 45, 39  ⊢  
  : , : , :
32instantiation40, 41, 42  ⊢  
  : , : , :
33instantiation54, 52, 43  ⊢  
  : , : , :
34instantiation54, 55, 44  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
36theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
37instantiation54, 45, 46  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
39instantiation54, 47, 48  ⊢  
  : , : , :
40axiom  ⊢  
 proveit.logic.equality.equals_transitivity
41instantiation49, 50  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.numerals.decimals.add_2_1
43instantiation54, 55, 51  ⊢  
  : , : , :
44theorem  ⊢  
 proveit.numbers.numerals.decimals.nat6
45theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
46assumption  ⊢  
47theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
48instantiation54, 52, 53  ⊢  
  : , : , :
49axiom  ⊢  
 proveit.logic.equality.substitution
50theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
51theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
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.nat1
*equality replacement requirements