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, b, f, i, j, k, l
from proveit.core_expr_types.tuples import shift_equiv_both
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, b], instance_expr = 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))]), 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, b \in \mathbb{Z}}~\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)\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: 54 body: 2
1	ExprTuple	54
2	Operation	operator: 9 operand: 4
3	ExprTuple	4
4	Lambda	parameters: 5 body: 6
5	ExprTuple	71, 73
6	Conditional	value: 7 condition: 8
7	Operation	operator: 9 operand: 12
8	Operation	operator: 23 operands: 11
9	Literal
10	ExprTuple	12
11	ExprTuple	13, 14
12	Lambda	parameters: 15 body: 16
13	Operation	operator: 32 operands: 17
14	Operation	operator: 32 operands: 18
15	ExprTuple	70, 68, 58, 59
16	Conditional	value: 19 condition: 20
17	ExprTuple	71, 21
18	ExprTuple	73, 21
19	Operation	operator: 35 operands: 22
20	Operation	operator: 23 operands: 24
21	Literal
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	27, 28, 29
25	ExprTuple	30
26	ExprTuple	31
27	Operation	operator: 32 operands: 33
28	Operation	operator: 35 operands: 34
29	Operation	operator: 35 operands: 36
30	ExprRange	lambda_map: 37 start_index: 70 end_index: 68
31	ExprRange	lambda_map: 38 start_index: 58 end_index: 59
32	Literal
33	ExprTuple	39, 40
34	ExprTuple	41, 42
35	Literal
36	ExprTuple	43, 44
37	Lambda	parameter: 72 body: 45
38	Lambda	parameter: 72 body: 47
39	Operation	operator: 66 operands: 48
40	Literal
41	Operation	operator: 66 operands: 49
42	Operation	operator: 66 operands: 50
43	Operation	operator: 66 operands: 51
44	Operation	operator: 66 operands: 52
45	Operation	operator: 54 operand: 60
46	ExprTuple	72
47	Operation	operator: 54 operand: 61
48	ExprTuple	56, 57
49	ExprTuple	70, 71
50	ExprTuple	58, 73
51	ExprTuple	68, 71
52	ExprTuple	59, 73
53	ExprTuple	60
54	Variable
55	ExprTuple	61
56	Operation	operator: 66 operands: 62
57	Operation	operator: 63 operand: 70
58	Variable
59	Variable
60	Operation	operator: 66 operands: 65
61	Operation	operator: 66 operands: 67
62	ExprTuple	68, 69
63	Literal
64	ExprTuple	70
65	ExprTuple	72, 71
66	Literal
67	ExprTuple	72, 73
68	Variable
69	Literal
70	Variable
71	Variable
72	Variable
73	Variable