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 type	requirements	statement
0	instantiation	1, 2, 3	⊢
	: , : , :
1	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	4, 24, 6, 8, 10, 11	⊢
	: , : , : , : , : , : , :
3	instantiation	5, 6, 7, 24, 8, 9, 10, 11, 12^*	⊢
	: , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.addition.leftward_commutation
5	theorem		⊢
	proveit.numbers.addition.association
6	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
7	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
8	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
9	instantiation	13	⊢
	: , :
10	instantiation	27, 15, 14	⊢
	: , : , :
11	instantiation	27, 15, 16	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
14	instantiation	27, 18, 17	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
16	instantiation	27, 18, 19	⊢
	: , : , :
17	instantiation	27, 21, 20	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
19	instantiation	27, 21, 22	⊢
	: , : , :
20	instantiation	27, 23, 24	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
22	instantiation	25, 26	⊢
	:
23	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
24	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
25	theorem		⊢
	proveit.numbers.negation.int_closure
26	instantiation	27, 28, 29	⊢
	: , : , :
27	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
28	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
29	assumption		⊢
^*equality replacement requirements