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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, 13, 12, 38, 15, 14, 16, 17, 5  ⊢  
  : , : , : , : , : , :
3instantiation6, 12, 13, 14, 15, 16, 17, 7, 8*  ⊢  
  : , : , : , : , :
4theorem  ⊢  
 proveit.numbers.multiplication.disassociation
5instantiation43, 22, 9  ⊢  
  : , : , :
6theorem  ⊢  
 proveit.numbers.multiplication.mult_neg_any
7instantiation43, 22, 10  ⊢  
  : , : , :
8instantiation11, 12, 13, 14, 15, 16, 17  ⊢  
  : , : , : , :
9instantiation43, 26, 18  ⊢  
  : , : , :
10instantiation43, 26, 19  ⊢  
  : , : , :
11theorem  ⊢  
 proveit.numbers.multiplication.elim_one_any
12theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2
13axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
14instantiation20  ⊢  
  : , :
15theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
16instantiation43, 22, 21  ⊢  
  : , : , :
17instantiation43, 22, 23  ⊢  
  : , : , :
18instantiation43, 25, 24  ⊢  
  : , : , :
19instantiation43, 25, 32  ⊢  
  : , : , :
20theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
21instantiation43, 26, 27  ⊢  
  : , : , :
22theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
23instantiation28, 29, 30  ⊢  
  : , : , :
24instantiation31, 32  ⊢  
  :
25theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
26theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
27instantiation43, 33, 34  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
29instantiation35, 36  ⊢  
  : , :
30axiom  ⊢  
 proveit.physics.quantum.QPE._t_in_natural_pos
31theorem  ⊢  
 proveit.numbers.negation.int_closure
32instantiation43, 37, 38  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
34instantiation39, 40, 41  ⊢  
  : , :
35theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
36theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
37theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
38theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
39theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
40instantiation43, 44, 42  ⊢  
  : , : , :
41instantiation43, 44, 45  ⊢  
  : , : , :
42theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
43theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
45theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
*equality replacement requirements