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

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(a, Conditional(Forall(instance_param_or_params = [i, j, k, l], instance_expr = shift_equiv, conditions = [InSet(subtract(Add(j, one), i), Natural), Equals(k, subtract(i, a)), Equals(l, subtract(j, a))]), InSet(a, 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(a \mapsto \left\{\forall_{i, j, k, l~|~\left(\left(j + 1\right) - i\right) \in \mathbb{N}, k = \left(i - a\right), l = \left(j - a\right)}~\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)\right) \textrm{ if } a \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	parameter: 59 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 24 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	59, 9
8	Lambda	parameters: 10 body: 11
9	Literal
10	ExprTuple	57, 55, 33, 35
11	Conditional	value: 12 condition: 13
12	Operation	operator: 27 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 18
15	Literal
16	ExprTuple	19, 20, 21
17	ExprTuple	22
18	ExprTuple	23
19	Operation	operator: 24 operands: 25
20	Operation	operator: 27 operands: 26
21	Operation	operator: 27 operands: 28
22	ExprRange	lambda_map: 29 start_index: 57 end_index: 55
23	ExprRange	lambda_map: 30 start_index: 33 end_index: 35
24	Literal
25	ExprTuple	31, 32
26	ExprTuple	33, 34
27	Literal
28	ExprTuple	35, 36
29	Lambda	parameter: 58 body: 37
30	Lambda	parameter: 58 body: 38
31	Operation	operator: 53 operands: 39
32	Literal
33	Variable
34	Operation	operator: 53 operands: 40
35	Variable
36	Operation	operator: 53 operands: 41
37	Operation	operator: 43 operand: 58
38	Operation	operator: 43 operand: 48
39	ExprTuple	45, 46
40	ExprTuple	57, 47
41	ExprTuple	55, 47
42	ExprTuple	58
43	Variable
44	ExprTuple	48
45	Operation	operator: 53 operands: 49
46	Operation	operator: 51 operand: 57
47	Operation	operator: 51 operand: 59
48	Operation	operator: 53 operands: 54
49	ExprTuple	55, 56
50	ExprTuple	57
51	Literal
52	ExprTuple	59
53	Literal
54	ExprTuple	58, 59
55	Variable
56	Literal
57	Variable
58	Variable
59	Variable