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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, 51, 6, 7, 8, 9, 11, 15  ⊢  
  : , : , : , : , : , :
3instantiation10, 15, 11, 12  ⊢  
  : , : , :
4theorem  ⊢  
 proveit.numbers.addition.disassociation
5theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
6axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
7instantiation13  ⊢  
  : , :
8theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
9instantiation14, 15  ⊢  
  :
10theorem  ⊢  
 proveit.numbers.addition.subtraction.add_cancel_triple_31
11instantiation49, 18, 16  ⊢  
  : , : , :
12instantiation17  ⊢  
  :
13theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
14theorem  ⊢  
 proveit.numbers.negation.complex_closure
15instantiation49, 18, 19  ⊢  
  : , : , :
16instantiation28, 20  ⊢  
  :
17axiom  ⊢  
 proveit.logic.equality.equals_reflexivity
18theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
19instantiation21, 22, 33  ⊢  
  : , :
20instantiation23, 24, 25, 26  ⊢  
  : , : , :
21theorem  ⊢  
 proveit.numbers.multiplication.mult_real_closure_bin
22instantiation49, 41, 27  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.all_in_interval_cc__is__real
24instantiation28, 29  ⊢  
  :
25theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.zero_is_real
26assumption  ⊢  
27instantiation49, 30, 31  ⊢  
  : , : , :
28theorem  ⊢  
 proveit.numbers.negation.real_closure
29instantiation32, 33, 34, 35  ⊢  
  : , :
30theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
31instantiation36, 37, 38  ⊢  
  : , :
32theorem  ⊢  
 proveit.numbers.division.div_real_closure
33instantiation49, 39, 40  ⊢  
  : , : , :
34instantiation49, 41, 42  ⊢  
  : , : , :
35instantiation43, 46  ⊢  
  :
36theorem  ⊢  
 proveit.numbers.division.div_rational_pos_closure
37instantiation49, 45, 44  ⊢  
  : , : , :
38instantiation49, 45, 46  ⊢  
  : , : , :
39theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
40theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
41theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
42instantiation49, 47, 48  ⊢  
  : , : , :
43theorem  ⊢  
 proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
44theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat1
45theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
46theorem  ⊢  
 proveit.numbers.numerals.decimals.posnat2
47theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
48instantiation49, 50, 51  ⊢  
  : , : , :
49theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
51theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2