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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, 7, 44, 39, 9, 5, 10, 25, 24  ⊢  
  : , : , : , : , : , :
3instantiation6, 39, 44, 7, 8, 9, 10, 25, 24, 11*  ⊢  
  : , : , : , : , : , :
4theorem  ⊢  
 proveit.numbers.addition.disassociation
5instantiation12  ⊢  
  : , :
6theorem  ⊢  
 proveit.numbers.addition.association
7axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
8instantiation12  ⊢  
  : , :
9theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
10instantiation42, 30, 13  ⊢  
  : , : , :
11instantiation14, 15, 16  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13instantiation17, 18, 19  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.logic.equality.sub_right_side_into
15instantiation20, 24, 21, 22  ⊢  
  : , : , :
16instantiation23, 24, 25  ⊢  
  : , :
17theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
18instantiation26, 27  ⊢  
  : , :
19theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
20theorem  ⊢  
 proveit.numbers.addition.subtraction.subtract_from_add_reversed
21instantiation42, 30, 28  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.numerals.decimals.add_1_1
23theorem  ⊢  
 proveit.numbers.addition.commutation
24instantiation42, 30, 29  ⊢  
  : , : , :
25instantiation42, 30, 31  ⊢  
  : , : , :
26theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
27theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
28instantiation42, 34, 32  ⊢  
  : , : , :
29instantiation42, 34, 33  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
31instantiation42, 34, 35  ⊢  
  : , : , :
32instantiation42, 37, 41  ⊢  
  : , : , :
33instantiation42, 37, 36  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
35instantiation42, 37, 38  ⊢  
  : , : , :
36instantiation42, 43, 39  ⊢  
  : , : , :
37theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
38instantiation40, 41  ⊢  
  :
39theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
40theorem  ⊢  
 proveit.numbers.negation.int_closure
41instantiation42, 43, 44  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
43theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
44theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
*equality replacement requirements