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 ExprTuple, Lambda, a, f, 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(f, Forall(instance_param_or_params = [a], instance_expr = 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))]), domain = 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(f \mapsto \left[\forall_{a \in \mathbb{Z}}~\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)\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	parameter: 47 body: 3
2	ExprTuple	47
3	Operation	operator: 9 operand: 5
4	ExprTuple	5
5	Lambda	parameter: 63 body: 6
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operand: 12
8	Operation	operator: 28 operands: 11
9	Literal
10	ExprTuple	12
11	ExprTuple	63, 13
12	Lambda	parameters: 14 body: 15
13	Literal
14	ExprTuple	61, 59, 37, 39
15	Conditional	value: 16 condition: 17
16	Operation	operator: 31 operands: 18
17	Operation	operator: 19 operands: 20
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	23, 24, 25
21	ExprTuple	26
22	ExprTuple	27
23	Operation	operator: 28 operands: 29
24	Operation	operator: 31 operands: 30
25	Operation	operator: 31 operands: 32
26	ExprRange	lambda_map: 33 start_index: 61 end_index: 59
27	ExprRange	lambda_map: 34 start_index: 37 end_index: 39
28	Literal
29	ExprTuple	35, 36
30	ExprTuple	37, 38
31	Literal
32	ExprTuple	39, 40
33	Lambda	parameter: 62 body: 41
34	Lambda	parameter: 62 body: 42
35	Operation	operator: 57 operands: 43
36	Literal
37	Variable
38	Operation	operator: 57 operands: 44
39	Variable
40	Operation	operator: 57 operands: 45
41	Operation	operator: 47 operand: 62
42	Operation	operator: 47 operand: 52
43	ExprTuple	49, 50
44	ExprTuple	61, 51
45	ExprTuple	59, 51
46	ExprTuple	62
47	Variable
48	ExprTuple	52
49	Operation	operator: 57 operands: 53
50	Operation	operator: 55 operand: 61
51	Operation	operator: 55 operand: 63
52	Operation	operator: 57 operands: 58
53	ExprTuple	59, 60
54	ExprTuple	61
55	Literal
56	ExprTuple	63
57	Literal
58	ExprTuple	62, 63
59	Variable
60	Literal
61	Variable
62	Variable
63	Variable