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, IndexedVar, Variable, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import And, Forall, Not, Or
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Forall(instance_param_or_params = [A_1_to_m], instance_expr = And(A_1_to_m), condition = Not(Or(ExprRange(sub_expr1, Not(IndexedVar(A, sub_expr1)), one, m))))

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_{1}, A_{2}, \ldots, A_{m}~|~\lnot \left((\lnot A_{1}) \lor  (\lnot A_{2}) \lor  \ldots \lor  (\lnot A_{m})\right)}~\left(A_{1} \land  A_{2} \land  \ldots \land  A_{m}\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: 8 body: 4
4	Conditional	value: 5 condition: 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 20 operand: 11
7	Literal
8	ExprTuple	10
9	ExprTuple	11
10	ExprRange	lambda_map: 12 start_index: 17 end_index: 18
11	Operation	operator: 13 operands: 14
12	Lambda	parameter: 25 body: 22
13	Literal
14	ExprTuple	15
15	ExprRange	lambda_map: 16 start_index: 17 end_index: 18
16	Lambda	parameter: 25 body: 19
17	Literal
18	Variable
19	Operation	operator: 20 operand: 22
20	Literal
21	ExprTuple	22
22	IndexedVar	variable: 23 index: 25
23	Variable
24	ExprTuple	25
25	Variable