Expression of type ExprTuple

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, ExprTuple, Lambda, a, i, j, k, l
from proveit.core_expr_types.tuples import neg_shift_equiv
from proveit.logic import And, Equals, InSet
from proveit.numbers import Natural, one, subtract

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([i, j, k, l], Conditional(neg_shift_equiv, And(InSet(subtract(subtract(j, one), i), Natural), Equals(k, subtract(i, a)), Equals(l, subtract(j, a))))))

expr:

# 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(\left(i, j, k, l\right) \mapsto \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) \textrm{ if } \left(\left(j - 1\right) - i\right) \in \mathbb{N} ,  k = \left(i - a\right) ,  l = \left(j - a\right)\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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