Expression of type And

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, B, ExprRange, IndexedVar, Variable, m
from proveit.logic import And, Boolean, Implies, InSet, Not, Or
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = IndexedVar(A, sub_expr1)
sub_expr3 = IndexedVar(B, sub_expr1)
expr = And(ExprRange(sub_expr1, InSet(sub_expr2, Boolean), one, m), ExprRange(sub_expr1, InSet(sub_expr3, Boolean), one, m), Or(ExprRange(sub_expr1, Not(sub_expr2), one, m)), ExprRange(sub_expr1, Implies(sub_expr2, sub_expr3), 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())

\left(A_{1} \in \mathbb{B}\right) \land  \left(A_{2} \in \mathbb{B}\right) \land  \ldots \land  \left(A_{m} \in \mathbb{B}\right)\land \left(B_{1} \in \mathbb{B}\right) \land  \left(B_{2} \in \mathbb{B}\right) \land  \ldots \land  \left(B_{m} \in \mathbb{B}\right) \land \left((\lnot A_{1}) \lor  (\lnot A_{2}) \lor  \ldots \lor  (\lnot A_{m})\right)\land \left(A_{1} \Rightarrow B_{1}\right) \land  \left(A_{2} \Rightarrow B_{2}\right) \land  \ldots \land  \left(A_{m} \Rightarrow B_{m}\right)

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4, 5, 6
3	ExprRange	lambda_map: 7 start_index: 20 end_index: 21
4	ExprRange	lambda_map: 8 start_index: 20 end_index: 21
5	Operation	operator: 9 operands: 10
6	ExprRange	lambda_map: 11 start_index: 20 end_index: 21
7	Lambda	parameter: 33 body: 12
8	Lambda	parameter: 33 body: 13
9	Literal
10	ExprTuple	14
11	Lambda	parameter: 33 body: 15
12	Operation	operator: 17 operands: 16
13	Operation	operator: 17 operands: 18
14	ExprRange	lambda_map: 19 start_index: 20 end_index: 21
15	Operation	operator: 22 operands: 23
16	ExprTuple	30, 24
17	Literal
18	ExprTuple	26, 24
19	Lambda	parameter: 33 body: 25
20	Literal
21	Variable
22	Literal
23	ExprTuple	30, 26
24	Literal
25	Operation	operator: 27 operand: 30
26	IndexedVar	variable: 29 index: 33
27	Literal
28	ExprTuple	30
29	Variable
30	IndexedVar	variable: 31 index: 33
31	Variable
32	ExprTuple	33
33	Variable