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