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, 4, 5, 6, 7^*	, ⊢
	: , : , : , : , :
1	theorem		⊢
	proveit.numbers.summation.sum_split_after
2	reference	33	⊢
3	instantiation	57, 58, 8	⊢
	: , : , :
4	reference	52	⊢
5	instantiation	9, 10, 11	, ⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.numerals.decimals.less_8_9
7	instantiation	12, 13, 14	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.numerals.decimals.nat8
9	theorem		⊢
	proveit.logic.equality.sub_right_side_into
10	instantiation	15, 16, 38, 17, 18, 19	, ⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.add_7_1
12	axiom		⊢
	proveit.logic.equality.equals_transitivity
13	instantiation	53, 20	⊢
	: , : , :
14	instantiation	21, 52, 22^*	⊢
	: , :
15	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right
16	instantiation	57, 46, 23	⊢
	: , : , :
17	instantiation	57, 46, 24	⊢
	: , : , :
18	assumption		⊢
19	instantiation	25, 42	⊢
	:
20	modus ponens	26, 27	⊢
21	axiom		⊢
	proveit.numbers.summation.sum_single
22	instantiation	28, 29, 30, 31, 32	⊢
	: , : , :
23	instantiation	57, 51, 33	⊢
	: , : , :
24	instantiation	57, 51, 34	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
26	instantiation	35, 36	⊢
	: , : , : , : , : , :
27	generalization	37	⊢
28	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
29	instantiation	57, 40, 38	⊢
	: , : , :
30	instantiation	57, 40, 39	⊢
	: , : , :
31	instantiation	57, 40, 41	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.add_7_2
33	assumption		⊢
34	instantiation	57, 58, 42	⊢
	: , : , :
35	axiom		⊢
	proveit.core_expr_types.lambda_maps.lambda_substitution
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
37	instantiation	53, 43	⊢
	: , : , :
38	instantiation	57, 46, 44	⊢
	: , : , :
39	instantiation	57, 46, 45	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
41	instantiation	57, 46, 47	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
43	instantiation	53, 48	⊢
	: , : , :
44	instantiation	57, 51, 49	⊢
	: , : , :
45	instantiation	57, 51, 50	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
47	instantiation	57, 51, 52	⊢
	: , : , :
48	instantiation	53, 54	⊢
	: , : , :
49	instantiation	57, 58, 55	⊢
	: , : , :
50	instantiation	57, 58, 56	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
52	instantiation	57, 58, 59	⊢
	: , : , :
53	axiom		⊢
	proveit.logic.equality.substitution
54	theorem		⊢
	proveit.numbers.numerals.decimals.add_8_1
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat7
56	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
57	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
58	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat9
^*equality replacement requirements