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	21	⊢
2	instantiation	3, 4, 5	, ⊢
	: , : , :
3	axiom		⊢
	proveit.logic.equality.equals_transitivity
4	instantiation	21, 6, 7^, 8^	⊢
	: , : , :
5	instantiation	9, 10	, ⊢
	: , :
6	modus ponens	11, 12	⊢
7	instantiation	13, 42	⊢
	: , :
8	instantiation	13, 42	⊢
	: , :
9	theorem		⊢
	proveit.logic.equality.equals_reversal
10	modus ponens	14, 15	, ⊢
11	instantiation	16, 24	⊢
	: , : , : , : , : , : , :
12	generalization	17	⊢
13	theorem		⊢
	proveit.core_expr_types.conditionals.satisfied_condition_reduction
14	instantiation	18, 24, 30, 32	⊢
	: , : , : , : , : , : , : , :
15	modus ponens	19, 20	⊢
16	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
17	instantiation	21, 22	, ⊢
	: , : , :
18	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum_with_scalar_mult
19	instantiation	23, 24, 30	⊢
	: , : , : , : , : , :
20	generalization	25	⊢
21	axiom		⊢
	proveit.logic.equality.substitution
22	instantiation	26, 27, 28	, ⊢
	: , :
23	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
24	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
25	instantiation	29, 30, 34, 31	, ⊢
	: , : , : , :
26	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
27	instantiation	47, 33, 32	⊢
	: , : , :
28	instantiation	47, 33, 34	⊢
	: , : , :
29	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
30	instantiation	35, 36	⊢
	:
31	assumption		⊢
32	assumption		⊢
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
34	instantiation	47, 37, 38	⊢
	: , : , :
35	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
36	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
38	instantiation	47, 39, 40	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
40	instantiation	47, 41, 42	⊢
	: , : , :
41	instantiation	43, 44, 45	⊢
	: , :
42	assumption		⊢
43	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
44	instantiation	47, 48, 46	⊢
	: , : , :
45	instantiation	47, 48, 49	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
47	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
^*equality replacement requirements