Expression of type Lambda

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 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 = 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())

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]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 46 body: 2
1	ExprTuple	46
2	Operation	operator: 8 operand: 4
3	ExprTuple	4
4	Lambda	parameter: 62 body: 5
5	Conditional	value: 6 condition: 7
6	Operation	operator: 8 operand: 11
7	Operation	operator: 27 operands: 10
8	Literal
9	ExprTuple	11
10	ExprTuple	62, 12
11	Lambda	parameters: 13 body: 14
12	Literal
13	ExprTuple	60, 58, 36, 38
14	Conditional	value: 15 condition: 16
15	Operation	operator: 30 operands: 17
16	Operation	operator: 18 operands: 19
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	22, 23, 24
20	ExprTuple	25
21	ExprTuple	26
22	Operation	operator: 27 operands: 28
23	Operation	operator: 30 operands: 29
24	Operation	operator: 30 operands: 31
25	ExprRange	lambda_map: 32 start_index: 60 end_index: 58
26	ExprRange	lambda_map: 33 start_index: 36 end_index: 38
27	Literal
28	ExprTuple	34, 35
29	ExprTuple	36, 37
30	Literal
31	ExprTuple	38, 39
32	Lambda	parameter: 61 body: 40
33	Lambda	parameter: 61 body: 41
34	Operation	operator: 56 operands: 42
35	Literal
36	Variable
37	Operation	operator: 56 operands: 43
38	Variable
39	Operation	operator: 56 operands: 44
40	Operation	operator: 46 operand: 61
41	Operation	operator: 46 operand: 51
42	ExprTuple	48, 49
43	ExprTuple	60, 50
44	ExprTuple	58, 50
45	ExprTuple	61
46	Variable
47	ExprTuple	51
48	Operation	operator: 56 operands: 52
49	Operation	operator: 54 operand: 60
50	Operation	operator: 54 operand: 62
51	Operation	operator: 56 operands: 57
52	ExprTuple	58, 59
53	ExprTuple	60
54	Literal
55	ExprTuple	62
56	Literal
57	ExprTuple	61, 62
58	Variable
59	Literal
60	Variable
61	Variable
62	Variable