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, b, i, j, k, l
from proveit.core_expr_types.tuples import shift_equiv_both
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_both, And(InSet(subtract(Add(j, one), i), Natural), Equals(Add(i, a), Add(k, b)), Equals(Add(j, a), Add(l, b))))))

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 + a\right), f\left(\left(i + 1\right) + a\right), \ldots, f\left(j + a\right)\right) = \left(f\left(k + b\right), f\left(\left(k + 1\right) + b\right), \ldots, f\left(l + b\right)\right) \textrm{ if } \left(\left(j + 1\right) - i\right) \in \mathbb{N} ,  \left(i + a\right) = \left(k + b\right) ,  \left(j + a\right) = \left(l + b\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, 42, 43
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: 54 end_index: 52
15	ExprRange	lambda_map: 22 start_index: 42 end_index: 43
16	Literal
17	ExprTuple	23, 24
18	ExprTuple	25, 26
19	Literal
20	ExprTuple	27, 28
21	Lambda	parameter: 56 body: 29
22	Lambda	parameter: 56 body: 31
23	Operation	operator: 50 operands: 32
24	Literal
25	Operation	operator: 50 operands: 33
26	Operation	operator: 50 operands: 34
27	Operation	operator: 50 operands: 35
28	Operation	operator: 50 operands: 36
29	Operation	operator: 38 operand: 44
30	ExprTuple	56
31	Operation	operator: 38 operand: 45
32	ExprTuple	40, 41
33	ExprTuple	54, 55
34	ExprTuple	42, 57
35	ExprTuple	52, 55
36	ExprTuple	43, 57
37	ExprTuple	44
38	Variable
39	ExprTuple	45
40	Operation	operator: 50 operands: 46
41	Operation	operator: 47 operand: 54
42	Variable
43	Variable
44	Operation	operator: 50 operands: 49
45	Operation	operator: 50 operands: 51
46	ExprTuple	52, 53
47	Literal
48	ExprTuple	54
49	ExprTuple	56, 55
50	Literal
51	ExprTuple	56, 57
52	Variable
53	Literal
54	Variable
55	Variable
56	Variable
57	Variable