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	6, 7, 4, 9, 5, 11, 12, 13, 10	, , , ⊢
	: , : , : , : , : , : , :
3	instantiation	6, 44, 47, 7, 8, 9, 10, 11, 12, 13	, , , ⊢
	: , : , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
5	instantiation	14	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.addition.leftward_commutation
7	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
8	instantiation	15	⊢
	: , :
9	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
10	instantiation	20, 16, 17	⊢
	: , :
11	instantiation	45, 31, 18	⊢
	: , : , :
12	instantiation	20, 24, 19	⊢
	: , :
13	instantiation	20, 24, 21	⊢
	: , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
15	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
16	instantiation	22, 23, 24, 25	⊢
	: , :
17	instantiation	45, 31, 26	⊢
	: , : , :
18	instantiation	45, 36, 27	⊢
	: , : , :
19	instantiation	45, 31, 28	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
21	instantiation	45, 31, 29	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.division.div_complex_closure
23	instantiation	45, 31, 30	⊢
	: , : , :
24	instantiation	45, 31, 32	⊢
	: , : , :
25	instantiation	33, 34	⊢
	:
26	instantiation	45, 36, 35	⊢
	: , : , :
27	assumption		⊢
28	assumption		⊢
29	instantiation	45, 36, 37	⊢
	: , : , :
30	instantiation	45, 39, 38	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
32	instantiation	45, 39, 40	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
34	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
35	assumption		⊢
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
37	assumption		⊢
38	instantiation	45, 42, 41	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
40	instantiation	45, 42, 43	⊢
	: , : , :
41	instantiation	45, 46, 44	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
43	instantiation	45, 46, 47	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
45	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat2