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	generalization	1	, ⊢
1	instantiation	2, 3, 4	, , ⊢
	: , : , :
2	theorem		⊢
	proveit.logic.equality.sub_left_side_into
3	instantiation	5, 6, 9, 7	, , ⊢
	: , : , : , :
4	instantiation	8, 9, 36, 10, 11, 16, 18, 19	, , ⊢
	: , : , : , : , : , : , : , : , : , :
5	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
6	instantiation	12, 14, 15, 16	⊢
	: , : , :
7	instantiation	13, 14, 15, 16, 17, 18, 19	, ⊢
	: , : , : , :
8	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
9	instantiation	20, 26, 21	⊢
	: , :
10	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
11	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
12	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
13	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
14	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
15	instantiation	24	⊢
	: , :
16	instantiation	22, 23	⊢
	:
17	instantiation	24	⊢
	: , :
18	assumption		⊢
19	assumption		⊢
20	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
21	instantiation	25, 26, 27	⊢
	: , :
22	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
23	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
24	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
25	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
26	instantiation	41, 29, 28	⊢
	: , : , :
27	instantiation	41, 29, 30	⊢
	: , : , :
28	instantiation	41, 32, 31	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
30	instantiation	41, 32, 33	⊢
	: , : , :
31	instantiation	41, 34, 35	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
33	instantiation	41, 42, 36	⊢
	: , : , :
34	instantiation	37, 38, 39	⊢
	: , :
35	assumption		⊢
36	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
37	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
38	instantiation	41, 42, 40	⊢
	: , : , :
39	instantiation	41, 42, 43	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
41	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
42	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat4