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	, , , ⊢
	: , :
1	theorem		⊢
	proveit.logic.equality.equals_reversal
2	modus ponens	3, 4	, , , ⊢
3	instantiation	5, 12, 15, 6	, ⊢
	: , : , : , : , : , : , : , :
4	modus ponens	7, 8	, ⊢
5	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum_with_scalar_mult
6	instantiation	19, 9, 10	, ⊢
	: , :
7	instantiation	11, 12, 15	⊢
	: , : , : , : , : , :
8	generalization	13	, ⊢
9	assumption		⊢
10	assumption		⊢
11	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
12	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
13	instantiation	14, 15, 16, 17	, , ⊢
	: , : , : , :
14	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
15	instantiation	18, 22, 23, 24	⊢
	: , : , :
16	instantiation	19, 29, 20	⊢
	: , :
17	instantiation	21, 22, 23, 24, 25, 26, 27	, ⊢
	: , : , : , :
18	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
19	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
20	instantiation	28, 29, 30	⊢
	: , :
21	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
22	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
23	instantiation	33	⊢
	: , :
24	instantiation	31, 32	⊢
	:
25	instantiation	33	⊢
	: , :
26	assumption		⊢
27	assumption		⊢
28	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
29	instantiation	47, 35, 34	⊢
	: , : , :
30	instantiation	47, 35, 36	⊢
	: , : , :
31	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
32	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
33	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
34	instantiation	47, 38, 37	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
36	instantiation	47, 38, 39	⊢
	: , : , :
37	instantiation	47, 40, 41	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
39	instantiation	47, 48, 42	⊢
	: , : , :
40	instantiation	43, 44, 45	⊢
	: , :
41	assumption		⊢
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
43	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
44	instantiation	47, 48, 46	⊢
	: , : , :
45	instantiation	47, 48, 49	⊢
	: , : , :
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