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 shift_equiv
from proveit.logic import And, Equals, InSet
from proveit.numbers import Add, Natural, one, subtract

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([i, j, k, l], Conditional(shift_equiv, And(InSet(subtract(Add(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	49, 47, 25, 27
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: 49 end_index: 47
15	ExprRange	lambda_map: 22 start_index: 25 end_index: 27
16	Literal
17	ExprTuple	23, 24
18	ExprTuple	25, 26
19	Literal
20	ExprTuple	27, 28
21	Lambda	parameter: 50 body: 29
22	Lambda	parameter: 50 body: 30
23	Operation	operator: 45 operands: 31
24	Literal
25	Variable
26	Operation	operator: 45 operands: 32
27	Variable
28	Operation	operator: 45 operands: 33
29	Operation	operator: 35 operand: 50
30	Operation	operator: 35 operand: 40
31	ExprTuple	37, 38
32	ExprTuple	49, 39
33	ExprTuple	47, 39
34	ExprTuple	50
35	Variable
36	ExprTuple	40
37	Operation	operator: 45 operands: 41
38	Operation	operator: 43 operand: 49
39	Operation	operator: 43 operand: 51
40	Operation	operator: 45 operands: 46
41	ExprTuple	47, 48
42	ExprTuple	49
43	Literal
44	ExprTuple	51
45	Literal
46	ExprTuple	50, 51
47	Variable
48	Literal
49	Variable
50	Variable
51	Variable