logo

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  ⊢  
  : , :
1theorem  ⊢  
 proveit.logic.equality.equals_reversal
2instantiation7, 3, 4  ⊢  
  : , : , :
3instantiation5, 6  ⊢  
  : , : , :
4instantiation7, 8, 9  ⊢  
  : , : , :
5axiom  ⊢  
 proveit.logic.equality.substitution
6instantiation10, 11  ⊢  
  :
7axiom  ⊢  
 proveit.logic.equality.equals_transitivity
8instantiation12, 39, 49, 15, 17, 16, 13, 18, 19  ⊢  
  : , : , : , : , : , :
9instantiation14, 15, 49, 16, 17, 18, 19  ⊢  
  : , : , : , :
10theorem  ⊢  
 proveit.numbers.multiplication.mult_zero_right
11instantiation47, 27, 20  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.addition.disassociation
13theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.zero_is_complex
14theorem  ⊢  
 proveit.numbers.addition.elim_zero_any
15axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
16theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
17instantiation21  ⊢  
  : , :
18instantiation23, 22  ⊢  
  :
19instantiation23, 24  ⊢  
  :
20instantiation47, 30, 25  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
22instantiation47, 27, 26  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.negation.complex_closure
24instantiation47, 27, 28  ⊢  
  : , : , :
25instantiation47, 33, 46  ⊢  
  : , : , :
26instantiation47, 30, 29  ⊢  
  : , : , :
27theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
28instantiation47, 30, 31  ⊢  
  : , : , :
29instantiation47, 33, 32  ⊢  
  : , : , :
30theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
31instantiation47, 33, 37  ⊢  
  : , : , :
32instantiation47, 34, 35  ⊢  
  : , : , :
33theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
34instantiation36, 37, 38  ⊢  
  : , :
35assumption  ⊢  
36theorem  ⊢  
 proveit.numbers.number_sets.integers.int_interval_within_int
37instantiation47, 48, 39  ⊢  
  : , : , :
38instantiation40, 41, 42  ⊢  
  : , :
39theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
40theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
41instantiation47, 43, 44  ⊢  
  : , : , :
42instantiation45, 46  ⊢  
  :
43theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
44theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
45theorem  ⊢  
 proveit.numbers.negation.int_closure
46instantiation47, 48, 49  ⊢  
  : , : , :
47theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
49theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2