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	axiom		⊢
	proveit.logic.equality.substitution
2	instantiation	3, 4, 12, 14, 16, 17, 5, 19, 6, 7^*	, , , , , ⊢
	: , : , : , : , : , : , : , : , : , :
3	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
4	assumption		⊢
5	instantiation	8, 10, 15, 17	⊢
	: , : , :
6	instantiation	9, 10, 15, 17, 18, 20, 21, 22, 23	, , , ⊢
	: , : , : , :
7	instantiation	11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23	, , , , ⊢
	: , : , : , : , : , : , : , : , : , :
8	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
9	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
10	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
11	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_disassociation
12	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
13	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
14	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
15	instantiation	25	⊢
	: , : , : , :
16	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
17	instantiation	24, 34	⊢
	:
18	instantiation	25	⊢
	: , : , : , :
19	instantiation	30, 31, 26	⊢
	: , : , :
20	instantiation	30, 31, 27	⊢
	: , : , :
21	instantiation	30, 31, 28	⊢
	: , : , :
22	instantiation	30, 31, 29	⊢
	: , : , :
23	instantiation	30, 31, 32	⊢
	: , : , :
24	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
25	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
26	assumption		⊢
27	assumption		⊢
28	assumption		⊢
29	assumption		⊢
30	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
31	instantiation	33, 34, 35	⊢
	: , : , :
32	assumption		⊢
33	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
34	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
35	instantiation	36, 37	⊢
	: , :
36	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
37	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
^*equality replacement requirements