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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  ⊢  
  : , :
1reference10  ⊢  
2instantiation3, 4, 5, 6  ⊢  
  : , : , : , :
3theorem  ⊢  
 proveit.logic.equality.four_chain_transitivity
4instantiation7, 34, 8  ⊢  
  : , :
5instantiation9  ⊢  
  :
6instantiation10, 11  ⊢  
  : , :
7theorem  ⊢  
 proveit.numbers.negation.distribute_neg_through_binary_sum
8instantiation58, 37, 12  ⊢  
  : , : , :
9axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
10theorem  ⊢  
 proveit.logic.equality.equals_reversal
11instantiation18, 13, 14  ⊢  
  : , : , :
12instantiation58, 40, 15  ⊢  
  : , : , :
13instantiation16, 17  ⊢  
  : , : , :
14instantiation18, 19, 20  ⊢  
  : , : , :
15instantiation58, 43, 48  ⊢  
  : , : , :
16axiom  ⊢  
 proveit.logic.equality.substitution
17instantiation21, 22  ⊢  
  :
18axiom  ⊢  
 proveit.logic.equality.equals_transitivity
19instantiation23, 50, 60, 26, 28, 27, 24, 29, 30  ⊢  
  : , : , : , : , : , :
20instantiation25, 26, 60, 27, 28, 29, 30  ⊢  
  : , : , : , :
21theorem  ⊢  
 proveit.numbers.multiplication.mult_zero_right
22instantiation58, 37, 31  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.addition.disassociation
24theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
25theorem  ⊢  
 proveit.numbers.addition.elim_zero_any
26axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
27theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
28instantiation32  ⊢  
  : , :
29instantiation33, 34  ⊢  
  :
30instantiation58, 37, 35  ⊢  
  : , : , :
31instantiation58, 40, 36  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
33theorem  ⊢  
 proveit.numbers.negation.complex_closure
34instantiation58, 37, 38  ⊢  
  : , : , :
35instantiation58, 40, 39  ⊢  
  : , : , :
36instantiation58, 43, 57  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
38instantiation58, 40, 41  ⊢  
  : , : , :
39instantiation58, 43, 42  ⊢  
  : , : , :
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
41instantiation58, 43, 44  ⊢  
  : , : , :
42instantiation56, 48  ⊢  
  :
43theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
44instantiation58, 45, 46  ⊢  
  : , : , :
45instantiation47, 48, 49  ⊢  
  : , :
46assumption  ⊢  
47theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
48instantiation58, 59, 50  ⊢  
  : , : , :
49instantiation51, 52, 53  ⊢  
  : , :
50theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
51theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
52instantiation58, 54, 55  ⊢  
  : , : , :
53instantiation56, 57  ⊢  
  :
54theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
55theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
56theorem  ⊢  
 proveit.numbers.negation.int_closure
57instantiation58, 59, 60  ⊢  
  : , : , :
58theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
59theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
60theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2