Expression of type Forall

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 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, Natural, one, subtract

# build up the expression from sub-expressions
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))])

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())

\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)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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