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Expression of type And

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.
%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
In [2]:
# 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:
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_{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)
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, 6
3ExprRangelambda_map: 7
start_index: 20
end_index: 21
4ExprRangelambda_map: 8
start_index: 20
end_index: 21
5Operationoperator: 9
operands: 10
6ExprRangelambda_map: 11
start_index: 20
end_index: 21
7Lambdaparameter: 33
body: 12
8Lambdaparameter: 33
body: 13
9Literal
10ExprTuple14
11Lambdaparameter: 33
body: 15
12Operationoperator: 17
operands: 16
13Operationoperator: 17
operands: 18
14ExprRangelambda_map: 19
start_index: 20
end_index: 21
15Operationoperator: 22
operands: 23
16ExprTuple30, 24
17Literal
18ExprTuple26, 24
19Lambdaparameter: 33
body: 25
20Literal
21Variable
22Literal
23ExprTuple30, 26
24Literal
25Operationoperator: 27
operand: 30
26IndexedVarvariable: 29
index: 33
27Literal
28ExprTuple30
29Variable
30IndexedVarvariable: 31
index: 33
31Variable
32ExprTuple33
33Variable