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 Conditional, 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 = 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())

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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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