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, Forall, InSet
from proveit.numbers import Add, Integer, Natural, one, subtract

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

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(a, b\right) \mapsto \left\{\forall_{i, j, k, l~|~\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)}~\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)\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z}\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	68, 70
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 9
5	Operation	operator: 20 operands: 8
6	Literal
7	ExprTuple	9
8	ExprTuple	10, 11
9	Lambda	parameters: 12 body: 13
10	Operation	operator: 29 operands: 14
11	Operation	operator: 29 operands: 15
12	ExprTuple	67, 65, 55, 56
13	Conditional	value: 16 condition: 17
14	ExprTuple	68, 18
15	ExprTuple	70, 18
16	Operation	operator: 32 operands: 19
17	Operation	operator: 20 operands: 21
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25, 26
22	ExprTuple	27
23	ExprTuple	28
24	Operation	operator: 29 operands: 30
25	Operation	operator: 32 operands: 31
26	Operation	operator: 32 operands: 33
27	ExprRange	lambda_map: 34 start_index: 67 end_index: 65
28	ExprRange	lambda_map: 35 start_index: 55 end_index: 56
29	Literal
30	ExprTuple	36, 37
31	ExprTuple	38, 39
32	Literal
33	ExprTuple	40, 41
34	Lambda	parameter: 69 body: 42
35	Lambda	parameter: 69 body: 44
36	Operation	operator: 63 operands: 45
37	Literal
38	Operation	operator: 63 operands: 46
39	Operation	operator: 63 operands: 47
40	Operation	operator: 63 operands: 48
41	Operation	operator: 63 operands: 49
42	Operation	operator: 51 operand: 57
43	ExprTuple	69
44	Operation	operator: 51 operand: 58
45	ExprTuple	53, 54
46	ExprTuple	67, 68
47	ExprTuple	55, 70
48	ExprTuple	65, 68
49	ExprTuple	56, 70
50	ExprTuple	57
51	Variable
52	ExprTuple	58
53	Operation	operator: 63 operands: 59
54	Operation	operator: 60 operand: 67
55	Variable
56	Variable
57	Operation	operator: 63 operands: 62
58	Operation	operator: 63 operands: 64
59	ExprTuple	65, 66
60	Literal
61	ExprTuple	67
62	ExprTuple	69, 68
63	Literal
64	ExprTuple	69, 70
65	Variable
66	Literal
67	Variable
68	Variable
69	Variable
70	Variable