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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, , ,  ⊢  
  : , : , :
1reference6  ⊢  
2instantiation4, 5  ⊢  
  : , : , :
3instantiation6, 7, 8, ,  ⊢  
  : , : , :
4axiom  ⊢  
 proveit.logic.equality.substitution
5instantiation9, 10  ⊢  
  :
6axiom  ⊢  
 proveit.logic.equality.equals_transitivity
7instantiation11, 12, 27, 13, 28, 17, 38, 18, 19, ,  ⊢  
  : , : , : , :
8instantiation14, 27, 45, 28, 15, 16, 17, 38, 18, 19, 20*, ,  ⊢  
  : , : , : , : , : , :
9theorem  ⊢  
 proveit.numbers.multiplication.mult_zero_left
10assumption  ⊢  
11theorem  ⊢  
 proveit.numbers.addition.elim_zero_any
12theorem  ⊢  
 proveit.numbers.numerals.decimals.nat4
13instantiation21  ⊢  
  : , : , : , :
14theorem  ⊢  
 proveit.numbers.addition.association
15instantiation33  ⊢  
  : , :
16instantiation33  ⊢  
  : , :
17instantiation22, 30, 38  ⊢  
  : , :
18assumption  ⊢  
19assumption  ⊢  
20instantiation23, 24, 25*  ⊢  
  : , :
21theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
22theorem  ⊢  
 proveit.numbers.multiplication.mult_complex_closure_bin
23theorem  ⊢  
 proveit.logic.equality.equals_reversal
24instantiation26, 27, 45, 48, 28, 29, 30, 31, 38, 32*  ⊢  
  : , : , : , : , : , :
25theorem  ⊢  
 proveit.numbers.numerals.decimals.add_2_1
26theorem  ⊢  
 proveit.numbers.multiplication.distribute_through_sum
27axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
28theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
29instantiation33  ⊢  
  : , :
30instantiation46, 35, 34  ⊢  
  : , : , :
31instantiation46, 35, 36  ⊢  
  : , : , :
32instantiation37, 38  ⊢  
  :
33theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
34instantiation46, 40, 39  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
36instantiation46, 40, 41  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
38assumption  ⊢  
39instantiation46, 43, 42  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
41instantiation46, 43, 44  ⊢  
  : , : , :
42instantiation46, 47, 45  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
44instantiation46, 47, 48  ⊢  
  : , : , :
45theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
46theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
47theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
48theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
*equality replacement requirements