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