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	⊢
	: , :
1	theorem		⊢
	proveit.logic.equality.equals_reversal
2	instantiation	7, 3, 4	⊢
	: , : , :
3	instantiation	5, 6	⊢
	: , : , :
4	instantiation	7, 8, 9	⊢
	: , : , :
5	axiom		⊢
	proveit.logic.equality.substitution
6	instantiation	10, 19	⊢
	:
7	axiom		⊢
	proveit.logic.equality.equals_transitivity
8	instantiation	11, 15, 14, 34, 17, 12, 18, 19	⊢
	: , : , : , : , : , :
9	instantiation	13, 34, 14, 15, 16, 17, 18, 19, 20^*	⊢
	: , : , : , : , : , :
10	theorem		⊢
	proveit.numbers.negation.double_negation
11	theorem		⊢
	proveit.numbers.addition.disassociation
12	instantiation	21	⊢
	: , :
13	theorem		⊢
	proveit.numbers.addition.association
14	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
15	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
16	instantiation	21	⊢
	: , :
17	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
18	instantiation	35, 23, 22	⊢
	: , : , :
19	instantiation	35, 23, 24	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
21	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
22	instantiation	35, 26, 25	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
24	instantiation	35, 26, 27	⊢
	: , : , :
25	instantiation	35, 29, 28	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
27	instantiation	35, 29, 30	⊢
	: , : , :
28	instantiation	31, 32	⊢
	:
29	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
30	instantiation	35, 33, 34	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.negation.int_closure
32	instantiation	35, 36, 37	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
34	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
35	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
36	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
37	assumption		⊢
^*equality replacement requirements