from the theory of proveit.logic.booleans.disjunction¶

In [1]:
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.
# import Expression classes needed to build the expression
from proveit import A, B, C, ExprRange, IndexedVar, Variable, l, m, n
from proveit.logic import And, Boolean, InSet
from proveit.numbers import one

In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = And(ExprRange(sub_expr1, InSet(IndexedVar(A, sub_expr1), Boolean), one, l), ExprRange(sub_expr1, InSet(IndexedVar(B, sub_expr1), Boolean), one, m), ExprRange(sub_expr1, InSet(IndexedVar(C, sub_expr1), Boolean), one, n))

expr:
In [3]:
# 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

In [4]:
# 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_{l} \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(C_{1} \in \mathbb{B}\right) \land  \left(C_{2} \in \mathbb{B}\right) \land  \ldots \land  \left(C_{n} \in \mathbb{B}\right)

In [5]:
stored_expr.style_options()

namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(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')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4, 5
3ExprRangelambda_map: 6
start_index: 11
end_index: 7
4ExprRangelambda_map: 8
start_index: 11
end_index: 9
5ExprRangelambda_map: 10
start_index: 11
end_index: 12
6Lambdaparameter: 28
body: 13
7Variable
8Lambdaparameter: 28
body: 14
9Variable
10Lambdaparameter: 28
body: 15
11Literal
12Variable
13Operationoperator: 18
operands: 16
14Operationoperator: 18
operands: 17
15Operationoperator: 18
operands: 19
16ExprTuple20, 23
17ExprTuple21, 23
18Literal
19ExprTuple22, 23
20IndexedVarvariable: 24
index: 28
21IndexedVarvariable: 25
index: 28
22IndexedVarvariable: 26
index: 28
23Literal
24Variable
25Variable
26Variable
27ExprTuple28
28Variable