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 neg_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(neg_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	58, 56, 47, 48
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: 46 end_index: 22
15	ExprRange	lambda_map: 23 start_index: 24 end_index: 25
16	Literal
17	ExprTuple	26, 27
18	ExprTuple	28, 29
19	Literal
20	ExprTuple	30, 31
21	Lambda	parameter: 64 body: 32
22	Operation	operator: 62 operand: 56
23	Lambda	parameter: 64 body: 34
24	Operation	operator: 62 operand: 47
25	Operation	operator: 62 operand: 48
26	Operation	operator: 54 operands: 37
27	Literal
28	Operation	operator: 54 operands: 38
29	Operation	operator: 54 operands: 39
30	Operation	operator: 54 operands: 40
31	Operation	operator: 54 operands: 41
32	Operation	operator: 43 operand: 49
33	ExprTuple	56
34	Operation	operator: 43 operand: 50
35	ExprTuple	47
36	ExprTuple	48
37	ExprTuple	45, 46
38	ExprTuple	58, 59
39	ExprTuple	47, 61
40	ExprTuple	56, 59
41	ExprTuple	48, 61
42	ExprTuple	49
43	Variable
44	ExprTuple	50
45	Operation	operator: 54 operands: 51
46	Operation	operator: 62 operand: 58
47	Variable
48	Variable
49	Operation	operator: 54 operands: 53
50	Operation	operator: 54 operands: 55
51	ExprTuple	56, 57
52	ExprTuple	58
53	ExprTuple	60, 59
54	Literal
55	ExprTuple	60, 61
56	Variable
57	Literal
58	Variable
59	Variable
60	Operation	operator: 62 operand: 64
61	Variable
62	Literal
63	ExprTuple	64
64	Variable