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	reference	9	⊢
2	instantiation	15, 52, 17, 16, 18, 19, 42, 3, 4^*	, , ⊢
	: , : , : , : , : , : , : , : , : , :
3	instantiation	5, 19, 52, 45	, ⊢
	: , : , : , :
4	instantiation	6, 7, 8	, , ⊢
	: , : , :
5	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
6	axiom		⊢
	proveit.logic.equality.equals_transitivity
7	instantiation	9, 10	, , ⊢
	: , : , :
8	instantiation	11, 12, 13, 47, 14^*	, , ⊢
	: , : , : , : , :
9	axiom		⊢
	proveit.logic.equality.substitution
10	instantiation	15, 52, 16, 17, 18, 19, 42, 45	, , ⊢
	: , : , : , : , : , : , : , : , : , :
11	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
12	instantiation	40, 20	⊢
	:
13	instantiation	43, 21, 22	, ⊢
	: , : , :
14	instantiation	23, 47, 24^*	⊢
	: , :
15	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
16	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
17	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
18	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
19	instantiation	25, 49	⊢
	:
20	theorem		⊢
	proveit.numbers.numerals.decimals.posnat9
21	instantiation	26, 30, 27, 49, 28^*	⊢
	: , : , :
22	instantiation	29, 30, 31, 32, 33, 34, 35	, ⊢
	: , : , : , :
23	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
24	instantiation	36, 47, 37, 38^, 39^	⊢
	: , : , :
25	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
26	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_cart_exps_within_cart_exp
27	instantiation	41	⊢
	: , :
28	theorem		⊢
	proveit.numbers.numerals.decimals.mult_3_3
29	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
30	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
31	instantiation	41	⊢
	: , :
32	instantiation	40, 49	⊢
	:
33	instantiation	41	⊢
	: , :
34	instantiation	43, 44, 42	⊢
	: , : , :
35	instantiation	43, 44, 45	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
37	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
38	instantiation	46, 47	⊢
	:
39	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
40	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
41	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
42	assumption		⊢
43	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
44	instantiation	48, 49, 50	⊢
	: , : , :
45	assumption		⊢
46	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
47	instantiation	51, 54, 52	⊢
	: , : , :
48	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
49	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
50	instantiation	53, 54	⊢
	: , :
51	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
52	assumption		⊢
53	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
54	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
^*equality replacement requirements