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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,  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.equals_transitivity
2instantiation4, 5, 48, 36, 6, 7, 10, 14, 8,  ⊢  
  : , : , : , : , : , :
3instantiation9, 14, 10, 11,  ⊢  
  : , : , :
4theorem  ⊢  
 proveit.numbers.addition.disassociation
5axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
6theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7instantiation12  ⊢  
  : , :
8instantiation13, 14  ⊢  
  :
9theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_23
10instantiation46, 17, 15,  ⊢  
  : , : , :
11instantiation16  ⊢  
  :
12theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13theorem  ⊢  
 proveit.numbers.negation.complex_closure
14instantiation46, 17, 18  ⊢  
  : , : , :
15instantiation46, 20, 19,  ⊢  
  : , : , :
16axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
17theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
18instantiation46, 20, 21  ⊢  
  : , : , :
19instantiation46, 23, 22,  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
21instantiation46, 23, 32  ⊢  
  : , : , :
22instantiation46, 24, 25,  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
24instantiation31, 26, 27  ⊢  
  : , :
25assumption  ⊢  
26instantiation46, 28, 29  ⊢  
  : , : , :
27instantiation37, 38, 30  ⊢  
  : , :
28instantiation31, 32, 33  ⊢  
  : , :
29assumption  ⊢  
30instantiation46, 34, 35  ⊢  
  : , : , :
31theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
32instantiation46, 47, 36  ⊢  
  : , : , :
33instantiation37, 38, 39  ⊢  
  : , :
34theorem  ⊢  
 proveit.numbers.number_sets.integers.neg_int_within_int
35instantiation40, 41  ⊢  
  :
36theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
37theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
38instantiation46, 42, 43  ⊢  
  : , : , :
39instantiation44, 45  ⊢  
  :
40theorem  ⊢  
 proveit.numbers.negation.int_neg_closure
41theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
42theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
43theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
44theorem  ⊢  
 proveit.numbers.negation.int_closure
45instantiation46, 47, 48  ⊢  
  : , : , :
46theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
47theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
48theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2