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, 3  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.equals_transitivity
2instantiation4, 5  ⊢  
  : , : , :
3instantiation6, 7, 8, 9*  ⊢  
  : , :
4axiom  ⊢  
 proveit.logic.equality.substitution
5instantiation10, 11  ⊢  
  :
6theorem  ⊢  
 proveit.numbers.negation.distribute_neg_through_binary_sum
7instantiation36, 19, 12  ⊢  
  : , : , :
8instantiation36, 19, 13  ⊢  
  : , : , :
9instantiation14, 15  ⊢  
  :
10theorem  ⊢  
 proveit.numbers.multiplication.elim_one_left
11instantiation36, 19, 16  ⊢  
  : , : , :
12instantiation36, 21, 17  ⊢  
  : , : , :
13instantiation36, 21, 18  ⊢  
  : , : , :
14theorem  ⊢  
 proveit.numbers.negation.double_negation
15instantiation36, 19, 20  ⊢  
  : , : , :
16instantiation36, 21, 22  ⊢  
  : , : , :
17instantiation36, 25, 30  ⊢  
  : , : , :
18instantiation36, 25, 31  ⊢  
  : , : , :
19theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
20instantiation23, 24, 38  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
22instantiation36, 25, 26  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.logic.sets.inclusion.unfold_subset_eq
24instantiation27, 28  ⊢  
  : , :
25theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
26instantiation29, 30, 31  ⊢  
  : , :
27theorem  ⊢  
 proveit.logic.sets.inclusion.relax_proper_subset
28theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.nat_pos_within_real
29theorem  ⊢  
 proveit.numbers.addition.add_int_closure_bin
30instantiation32, 33  ⊢  
  :
31instantiation36, 34, 35  ⊢  
  : , : , :
32theorem  ⊢  
 proveit.numbers.negation.int_closure
33instantiation36, 37, 38  ⊢  
  : , : , :
34theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
35theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
36theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
37theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_pos_within_int
38theorem  ⊢  
 proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
*equality replacement requirements