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	modus ponens	1, 2	, ⊢
1	instantiation	3, 4, 5, 6, 7, 8	⊢
	: , : , : , : , : , : , : , : , : , :
2	generalization	9	, ⊢
3	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation
4	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
5	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
6	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
7	instantiation	10, 33, 12, 13	⊢
	: , : , :
8	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
9	instantiation	11, 33, 12, 13, 14, 15, 16	, , ⊢
	: , : , : , :
10	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
11	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
12	instantiation	19	⊢
	: , :
13	instantiation	17, 18	⊢
	:
14	instantiation	19	⊢
	: , :
15	assumption		⊢
16	instantiation	20, 21	, ⊢
	:
17	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
18	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
19	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
20	assumption		⊢
21	instantiation	22, 23, 24	⊢
	:
22	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
23	instantiation	39, 25, 37	⊢
	: , : , :
24	instantiation	26, 27	⊢
	: , :
25	instantiation	28, 35, 36	⊢
	: , :
26	theorem		⊢
	proveit.numbers.ordering.relax_less
27	instantiation	29, 30, 31	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
29	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
30	instantiation	32, 33	⊢
	:
31	instantiation	34, 35, 36, 37	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
33	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
34	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
35	instantiation	39, 40, 38	⊢
	: , : , :
36	instantiation	39, 40, 41	⊢
	: , : , :
37	assumption		⊢
38	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
39	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
40	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat4