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	12	⊢
2	instantiation	3, 4, 5	, , , , , ⊢
	: , : , :
3	axiom		⊢
	proveit.logic.equality.equals_transitivity
4	instantiation	18, 6, 7, 8, 9, 24, 10, 26, 27, 28, 11	, , , , , ⊢
	: , : , : , : , : , : , : , : , : , :
5	instantiation	12, 13	, , , , ⊢
	: , : , :
6	instantiation	14, 42, 15	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
8	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
9	instantiation	16	⊢
	: , :
10	instantiation	16	⊢
	: , :
11	instantiation	17, 24, 19, 29	, ⊢
	: , : , : , :
12	axiom		⊢
	proveit.logic.equality.substitution
13	instantiation	18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29	, , , , ⊢
	: , : , : , : , : , : , : , : , : , :
14	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
15	assumption		⊢
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
17	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
18	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
19	assumption		⊢
20	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
21	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
22	instantiation	31	⊢
	: , : , :
23	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
24	instantiation	30, 39	⊢
	:
25	instantiation	31	⊢
	: , : , :
26	instantiation	35, 36, 32	⊢
	: , : , :
27	instantiation	35, 36, 33	⊢
	: , : , :
28	instantiation	35, 36, 34	⊢
	: , : , :
29	instantiation	35, 36, 37	⊢
	: , : , :
30	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
31	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
32	assumption		⊢
33	assumption		⊢
34	assumption		⊢
35	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
36	instantiation	38, 39, 40	⊢
	: , : , :
37	assumption		⊢
38	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
40	instantiation	41, 42	⊢
	: , :
41	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
42	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex