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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, 32, 6  ⊢  
  : , :
3instantiation7  ⊢  
  :
4instantiation8, 9  ⊢  
  : , :
5theorem  ⊢  
 proveit.numbers.negation.distribute_neg_through_binary_sum
6instantiation56, 35, 10  ⊢  
  : , : , :
7axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
8theorem  ⊢  
 proveit.logic.equality.equals_reversal
9instantiation16, 11, 12  ⊢  
  : , : , :
10instantiation56, 38, 13  ⊢  
  : , : , :
11instantiation14, 15  ⊢  
  : , : , :
12instantiation16, 17, 18  ⊢  
  : , : , :
13instantiation56, 41, 46  ⊢  
  : , : , :
14axiom  ⊢  
 proveit.logic.equality.substitution
15instantiation19, 20  ⊢  
  :
16axiom  ⊢  
 proveit.logic.equality.equals_transitivity
17instantiation21, 48, 58, 24, 26, 25, 22, 27, 28  ⊢  
  : , : , : , : , : , :
18instantiation23, 24, 58, 25, 26, 27, 28  ⊢  
  : , : , : , :
19theorem  ⊢  
 proveit.numbers.multiplication.mult_zero_right
20instantiation56, 35, 29  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.addition.disassociation
22theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
23theorem  ⊢  
 proveit.numbers.addition.elim_zero_any
24axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
25theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
26instantiation30  ⊢  
  : , :
27instantiation31, 32  ⊢  
  :
28instantiation56, 35, 33  ⊢  
  : , : , :
29instantiation56, 38, 34  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
31theorem  ⊢  
 proveit.numbers.negation.complex_closure
32instantiation56, 35, 36  ⊢  
  : , : , :
33instantiation56, 38, 37  ⊢  
  : , : , :
34instantiation56, 41, 55  ⊢  
  : , : , :
35theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
36instantiation56, 38, 39  ⊢  
  : , : , :
37instantiation56, 41, 40  ⊢  
  : , : , :
38theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
39instantiation56, 41, 42  ⊢  
  : , : , :
40instantiation54, 46  ⊢  
  :
41theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
42instantiation56, 43, 44  ⊢  
  : , : , :
43instantiation45, 46, 47  ⊢  
  : , :
44assumption  ⊢  
45theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
46instantiation56, 57, 48  ⊢  
  : , : , :
47instantiation49, 50, 51  ⊢  
  : , :
48theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
49theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
50instantiation56, 52, 53  ⊢  
  : , : , :
51instantiation54, 55  ⊢  
  :
52theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
53theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
54theorem  ⊢  
 proveit.numbers.negation.int_closure
55instantiation56, 57, 58  ⊢  
  : , : , :
56theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
57theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
58theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2