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, 42, 6, 16, 12, 17	⊢
	: , : , : , : , : , : , : , : , : , : , :
4	generalization	7	, ⊢
5	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation_with_scalar_mult
6	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
7	instantiation	8, 9, 10	, , ⊢
	: , : , :
8	theorem		⊢
	proveit.logic.equality.sub_left_side_into
9	instantiation	11, 12, 15, 13	, , ⊢
	: , : , : , :
10	instantiation	14, 15, 42, 16, 17, 22, 24, 25	, , ⊢
	: , : , : , : , : , : , : , : , : , :
11	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
12	instantiation	18, 20, 21, 22	⊢
	: , : , :
13	instantiation	19, 20, 21, 22, 23, 24, 25	, ⊢
	: , : , : , :
14	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
15	instantiation	26, 32, 27	⊢
	: , :
16	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
17	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
18	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
19	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
20	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
21	instantiation	30	⊢
	: , :
22	instantiation	28, 29	⊢
	:
23	instantiation	30	⊢
	: , :
24	assumption		⊢
25	assumption		⊢
26	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
27	instantiation	31, 32, 33	⊢
	: , :
28	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
29	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
30	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
31	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
32	instantiation	47, 35, 34	⊢
	: , : , :
33	instantiation	47, 35, 36	⊢
	: , : , :
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