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	, , , , ⊢
	: , : , :
1	reference	9	⊢
2	instantiation	37, 4	, , ⊢
	: , : , :
3	instantiation	5, 22, 6, 30, 7, 18, 8	, , , , ⊢
	: , : , : , : , : , : , : , : , : , :
4	instantiation	9, 10, 11	, , ⊢
	: , : , :
5	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
6	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
7	assumption		⊢
8	assumption		⊢
9	axiom		⊢
	proveit.logic.equality.equals_transitivity
10	instantiation	37, 12	, ⊢
	: , : , :
11	instantiation	13, 14	, , ⊢
	: , :
12	modus ponens	15, 16	, ⊢
13	theorem		⊢
	proveit.logic.equality.equals_reversal
14	modus ponens	17, 18	, , ⊢
15	instantiation	19, 29	⊢
	: , : , : , : , : , :
16	generalization	20	, ⊢
17	instantiation	21, 29, 30, 22	, ⊢
	: , : , : , : , : , : , :
18	modus ponens	23, 24	⊢
19	axiom		⊢
	proveit.core_expr_types.lambda_maps.lambda_substitution
20	instantiation	25, 26	, ⊢
	: , : , :
21	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum
22	instantiation	27, 48, 50	, ⊢
	: , :
23	instantiation	28, 29, 30	⊢
	: , : , : , : , : , :
24	generalization	31	⊢
25	axiom		⊢
	proveit.core_expr_types.conditionals.conditional_substitution
26	deduction	32	, ⊢
27	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
28	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
29	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
30	instantiation	33, 34	⊢
	:
31	instantiation	35, 36	, ⊢
	:
32	instantiation	37, 38	, ⊢
	: , : , :
33	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
34	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
35	assumption		⊢
36	instantiation	39, 40, 41	⊢
	:
37	axiom		⊢
	proveit.logic.equality.substitution
38	instantiation	42, 43, 44	, ⊢
	: , :
39	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
40	instantiation	62, 45, 60	⊢
	: , : , :
41	instantiation	46, 47	⊢
	: , :
42	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
43	instantiation	62, 49, 48	⊢
	: , : , :
44	instantiation	62, 49, 50	⊢
	: , : , :
45	instantiation	51, 58, 59	⊢
	: , :
46	theorem		⊢
	proveit.numbers.ordering.relax_less
47	instantiation	52, 53, 54	⊢
	: , : , :
48	assumption		⊢
49	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
50	assumption		⊢
51	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
52	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
53	instantiation	55, 56	⊢
	:
54	instantiation	57, 58, 59, 60	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
56	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
57	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
58	instantiation	62, 63, 61	⊢
	: , : , :
59	instantiation	62, 63, 64	⊢
	: , : , :
60	assumption		⊢
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
62	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
63	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
64	theorem		⊢
	proveit.numbers.numerals.decimals.nat4