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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  ⊢  
  : , : , :
1axiom  ⊢  
 proveit.logic.equality.substitution
2instantiation3, 27, 4, 5, 6, 7, 8, 9, 10, 11  ⊢  
  : , : , : , : , : , : , :
3theorem  ⊢  
 proveit.numbers.multiplication.leftward_commutation
4theorem  ⊢  
 proveit.numbers.numerals.decimals.nat1
5axiom  ⊢  
 proveit.numbers.number_sets.natural_numbers.zero_in_nats
6instantiation12  ⊢  
  : , :
7theorem  ⊢  
 proveit.core_expr_types.tuples.tuple_len_0_typical_eq
8instantiation25, 15, 13  ⊢  
  : , : , :
9instantiation25, 15, 14  ⊢  
  : , : , :
10theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.i_is_complex
11instantiation25, 15, 16  ⊢  
  : , : , :
12theorem  ⊢  
 proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13instantiation25, 20, 17  ⊢  
  : , : , :
14instantiation25, 18, 19  ⊢  
  : , : , :
15theorem  ⊢  
 proveit.numbers.number_sets.complex_numbers.real_within_complex
16instantiation25, 20, 21  ⊢  
  : , : , :
17instantiation25, 23, 22  ⊢  
  : , : , :
18theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.real_pos_within_real
19theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.pi_is_real_pos
20theorem  ⊢  
 proveit.numbers.number_sets.real_numbers.rational_within_real
21instantiation25, 23, 24  ⊢  
  : , : , :
22instantiation25, 26, 27  ⊢  
  : , : , :
23theorem  ⊢  
 proveit.numbers.number_sets.rational_numbers.int_within_rational
24assumption  ⊢  
25theorem  ⊢  
 proveit.logic.sets.inclusion.superset_membership_from_proper_subset
26theorem  ⊢  
 proveit.numbers.number_sets.integers.nat_within_int
27theorem  ⊢  
 proveit.numbers.numerals.decimals.nat2