Expression of type Forall

from the theory of proveit.logic.booleans.conjunction

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, ExprRange, Variable, i, j
from proveit.logic import And, Forall
from proveit.numbers import Add, LessEq, one

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [A], instance_expr = And(ExprRange(Variable("_a", latex_format = r"{_{-}a}"), A, i, j)), conditions = [A, LessEq(i, Add(j, one))])

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_{A~|~A, i \leq \left(j + 1\right)}~\left(A \land  A \land  ..\left(j - i - 2\right) \times.. \land  A\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	parameter: 17 body: 5
4	ExprTuple	17
5	Conditional	value: 6 condition: 7
6	Operation	operator: 9 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11
9	Literal
10	ExprTuple	17, 12
11	ExprRange	lambda_map: 13 start_index: 18 end_index: 23
12	Operation	operator: 14 operands: 15
13	Lambda	parameter: 20 body: 17
14	Literal
15	ExprTuple	18, 19
16	ExprTuple	20
17	Variable
18	Variable
19	Operation	operator: 21 operands: 22
20	Variable
21	Literal
22	ExprTuple	23, 24
23	Variable
24	Literal