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	theorem		⊢
	proveit.logic.equality.sub_right_side_into
2	instantiation	4, 30, 5	, , , ⊢
	: , :
3	instantiation	6, 7, 8	, , , ⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_from_double_neg
5	instantiation	38, 9, 37	, ⊢
	: , :
6	axiom		⊢
	proveit.logic.equality.equals_transitivity
7	instantiation	12, 10, 14, 13, 17, 15, 11, 20, 21	, , , ⊢
	: , : , : , : , : , :
8	instantiation	12, 13, 14, 15, 16, 17, 18, 19, 20, 21	, , , ⊢
	: , : , : , : , : , :
9	instantiation	49, 45, 44	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
11	instantiation	49, 27, 22	, ⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.multiplication.disassociation
13	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
14	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
15	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
16	instantiation	23	⊢
	: , :
17	instantiation	23	⊢
	: , :
18	instantiation	49, 27, 24	⊢
	: , : , :
19	instantiation	49, 27, 25	⊢
	: , : , :
20	instantiation	49, 27, 26	⊢
	: , : , :
21	instantiation	49, 27, 28	⊢
	: , : , :
22	instantiation	49, 29, 30	, ⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
24	instantiation	49, 34, 31	⊢
	: , : , :
25	instantiation	32, 33, 51	⊢
	: , : , :
26	instantiation	49, 34, 35	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
28	instantiation	49, 36, 37	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
30	instantiation	38, 39, 40	, ⊢
	: , :
31	instantiation	49, 43, 46	⊢
	: , : , :
32	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
33	instantiation	41, 42	⊢
	: , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
35	instantiation	49, 43, 44	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
37	assumption		⊢
38	theorem		⊢
	proveit.numbers.multiplication.mult_real_neg_from_left_neg
39	instantiation	49, 45, 46	⊢
	: , : , :
40	instantiation	49, 47, 48	⊢
	: , : , :
41	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
43	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_neg_within_rational
44	assumption		⊢
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
46	assumption		⊢
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
48	instantiation	49, 50, 51	⊢
	: , : , :
49	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
51	assumption		⊢