Expression of type Conditional ¶

from the theory of proveit.core_expr_types.tuples ¶

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, a, i, j, k, l
from proveit.core_expr_types.tuples import neg_shift_equiv
from proveit.logic import Equals, Forall, InSet
from proveit.numbers import Integer, Natural, one, subtract

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [i, j, k, l], instance_expr = neg_shift_equiv, conditions = [InSet(subtract(subtract(j, one), i), Natural), Equals(k, subtract(i, a)), Equals(l, subtract(j, a))]), InSet(a, Integer))

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{\forall_{i, j, k, l~|~\left(\left(j - 1\right) - i\right) \in \mathbb{N}, k = \left(i - a\right), l = \left(j - a\right)}~\left(\left(f\left(i\right), f\left(i - 1\right), \ldots, f\left(j\right)\right) = \left(f\left(k + a\right), f\left(\left(k - 1\right) + a\right), \ldots, f\left(l + a\right)\right)\right) \textrm{ if } a \in \mathbb{Z}\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 22 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	62, 7
6	Lambda	parameters: 8 body: 9
7	Literal
8	ExprTuple	60, 58, 47, 48
9	Conditional	value: 10 condition: 11
10	Operation	operator: 25 operands: 12
11	Operation	operator: 13 operands: 14
12	ExprTuple	15, 16
13	Literal
14	ExprTuple	17, 18, 19
15	ExprTuple	20
16	ExprTuple	21
17	Operation	operator: 22 operands: 23
18	Operation	operator: 25 operands: 24
19	Operation	operator: 25 operands: 26
20	ExprRange	lambda_map: 27 start_index: 50 end_index: 28
21	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
22	Literal
23	ExprTuple	32, 33
24	ExprTuple	47, 34
25	Literal
26	ExprTuple	48, 35
27	Lambda	parameter: 67 body: 36
28	Operation	operator: 64 operand: 58
29	Lambda	parameter: 67 body: 38
30	Operation	operator: 64 operand: 47
31	Operation	operator: 64 operand: 48
32	Operation	operator: 56 operands: 41
33	Literal
34	Operation	operator: 56 operands: 42
35	Operation	operator: 56 operands: 43
36	Operation	operator: 45 operand: 61
37	ExprTuple	58
38	Operation	operator: 45 operand: 52
39	ExprTuple	47
40	ExprTuple	48
41	ExprTuple	49, 50
42	ExprTuple	60, 51
43	ExprTuple	58, 51
44	ExprTuple	61
45	Variable
46	ExprTuple	52
47	Variable
48	Variable
49	Operation	operator: 56 operands: 53
50	Operation	operator: 64 operand: 60
51	Operation	operator: 64 operand: 62
52	Operation	operator: 56 operands: 57
53	ExprTuple	58, 59
54	ExprTuple	60
55	ExprTuple	62
56	Literal
57	ExprTuple	61, 62
58	Variable
59	Operation	operator: 64 operand: 66
60	Variable
61	Operation	operator: 64 operand: 67
62	Variable
63	ExprTuple	66
64	Literal
65	ExprTuple	67
66	Literal
67	Variable

Expression of type Conditional¶

from the theory of proveit.core_expr_types.tuples¶

Expression of type Conditional ¶

from the theory of proveit.core_expr_types.tuples ¶