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, b, 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, Natural, one, subtract

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

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}, \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)

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	56, 54, 44, 45
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: 56 end_index: 54
17	ExprRange	lambda_map: 24 start_index: 44 end_index: 45
18	Literal
19	ExprTuple	25, 26
20	ExprTuple	27, 28
21	Literal
22	ExprTuple	29, 30
23	Lambda	parameter: 58 body: 31
24	Lambda	parameter: 58 body: 33
25	Operation	operator: 52 operands: 34
26	Literal
27	Operation	operator: 52 operands: 35
28	Operation	operator: 52 operands: 36
29	Operation	operator: 52 operands: 37
30	Operation	operator: 52 operands: 38
31	Operation	operator: 40 operand: 46
32	ExprTuple	58
33	Operation	operator: 40 operand: 47
34	ExprTuple	42, 43
35	ExprTuple	56, 57
36	ExprTuple	44, 59
37	ExprTuple	54, 57
38	ExprTuple	45, 59
39	ExprTuple	46
40	Variable
41	ExprTuple	47
42	Operation	operator: 52 operands: 48
43	Operation	operator: 49 operand: 56
44	Variable
45	Variable
46	Operation	operator: 52 operands: 51
47	Operation	operator: 52 operands: 53
48	ExprTuple	54, 55
49	Literal
50	ExprTuple	56
51	ExprTuple	58, 57
52	Literal
53	ExprTuple	58, 59
54	Variable
55	Literal
56	Variable
57	Variable
58	Variable
59	Variable