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, 7, 40, 45, 9, 5, 10, 22, 21	⊢
	: , : , : , : , : , :
3	instantiation	6, 45, 40, 7, 8, 9, 10, 22, 21, 11^*	⊢
	: , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.addition.disassociation
5	instantiation	12	⊢
	: , :
6	theorem		⊢
	proveit.numbers.addition.association
7	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
8	instantiation	12	⊢
	: , :
9	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
10	instantiation	43, 30, 13	⊢
	: , : , :
11	instantiation	14, 15, 16	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13	instantiation	43, 36, 17	⊢
	: , : , :
14	theorem		⊢
	proveit.logic.equality.sub_right_side_into
15	instantiation	18, 26, 21, 19	⊢
	: , : , :
16	instantiation	20, 21, 22	⊢
	: , :
17	instantiation	43, 41, 23	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
19	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
20	theorem		⊢
	proveit.numbers.addition.commutation
21	instantiation	43, 30, 24	⊢
	: , : , :
22	instantiation	25, 26	⊢
	:
23	instantiation	43, 27, 28	⊢
	: , : , :
24	instantiation	43, 36, 29	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.negation.complex_closure
26	instantiation	43, 30, 31	⊢
	: , : , :
27	instantiation	32, 33, 34	⊢
	: , :
28	assumption		⊢
29	instantiation	43, 41, 35	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
31	instantiation	43, 36, 37	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
33	instantiation	43, 44, 38	⊢
	: , : , :
34	instantiation	43, 44, 39	⊢
	: , : , :
35	instantiation	43, 44, 40	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
37	instantiation	43, 41, 42	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat7
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
42	instantiation	43, 44, 45	⊢
	: , : , :
43	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements