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