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, 5	, ⊢
	: , : , :
3	instantiation	6, 19, 46, 7, 8, 24, 9, 10, 11, 17, 12	, , , , ⊢
	: , : , : , : , : , : , : , : , : , :
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	13, 14	, ⊢
	: , :
6	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
7	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
8	instantiation	15	⊢
	: , :
9	instantiation	15	⊢
	: , :
10	assumption		⊢
11	assumption		⊢
12	assumption		⊢
13	theorem		⊢
	proveit.logic.equality.equals_reversal
14	modus ponens	16, 17	, ⊢
15	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
16	instantiation	18, 23, 24, 19	⊢
	: , : , : , : , : , : , :
17	modus ponens	20, 21	⊢
18	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum
19	assumption		⊢
20	instantiation	22, 23, 24	⊢
	: , : , : , : , : , :
21	generalization	25	⊢
22	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
23	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
24	instantiation	26, 27	⊢
	:
25	instantiation	28, 29	, ⊢
	:
26	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
27	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
28	assumption		⊢
29	instantiation	30, 31, 32	⊢
	:
30	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
31	instantiation	47, 33, 45	⊢
	: , : , :
32	instantiation	34, 35	⊢
	: , :
33	instantiation	36, 43, 44	⊢
	: , :
34	theorem		⊢
	proveit.numbers.ordering.relax_less
35	instantiation	37, 38, 39	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
37	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
38	instantiation	40, 41	⊢
	:
39	instantiation	42, 43, 44, 45	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
41	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
42	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
43	instantiation	47, 48, 46	⊢
	: , : , :
44	instantiation	47, 48, 49	⊢
	: , : , :
45	assumption		⊢
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
47	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat4