Expression of type Forall

from the theory of proveit.logic.booleans.disjunction

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.logic import Boolean, Forall, InSet, Or
from proveit.numbers import Add, one, two

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(A, sub_expr1)
sub_expr3 = Add(m, one)
expr = Forall(instance_param_or_params = [ExprRange(sub_expr1, sub_expr2, one, Add(m, two))], instance_expr = InSet(Or(ExprRange(sub_expr1, sub_expr2, one, sub_expr3)), Boolean), condition = ExprRange(sub_expr1, InSet(sub_expr2, Boolean), one, sub_expr3))

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 + 2}~|~\left(A_{1} \in \mathbb{B}\right), \left(A_{2} \in \mathbb{B}\right), \ldots, \left(A_{m + 1} \in \mathbb{B}\right)}~\left(\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m + 1}\right) \in \mathbb{B}\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	6
5	Conditional	value: 7 condition: 8
6	ExprRange	lambda_map: 22 start_index: 31 end_index: 9
7	Operation	operator: 24 operands: 10
8	Operation	operator: 11 operands: 12
9	Operation	operator: 26 operands: 13
10	ExprTuple	14, 29
11	Literal
12	ExprTuple	15
13	ExprTuple	30, 16
14	Operation	operator: 17 operands: 18
15	ExprRange	lambda_map: 19 start_index: 31 end_index: 23
16	Literal
17	Literal
18	ExprTuple	20
19	Lambda	parameter: 34 body: 21
20	ExprRange	lambda_map: 22 start_index: 31 end_index: 23
21	Operation	operator: 24 operands: 25
22	Lambda	parameter: 34 body: 28
23	Operation	operator: 26 operands: 27
24	Literal
25	ExprTuple	28, 29
26	Literal
27	ExprTuple	30, 31
28	IndexedVar	variable: 32 index: 34
29	Literal
30	Variable
31	Literal
32	Variable
33	ExprTuple	34
34	Variable