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Expression of type And

from the theory of proveit.logic.sets.comprehension

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 ExprRange, IndexedVar, S, Variable, n, x
from proveit.core_expr_types import R__x_1_to_n
from proveit.logic import And, 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(x, sub_expr1), IndexedVar(S, sub_expr1)), one, n), R__x_1_to_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(x_{1} \in S_{1}\right) \land  \left(x_{2} \in S_{2}\right) \land  \ldots \land  \left(x_{n} \in S_{n}\right) \land R\left(x_{1}, x_{2}, \ldots, x_{n}\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
3ExprRangelambda_map: 5
start_index: 13
end_index: 14
4Operationoperator: 6
operands: 7
5Lambdaparameter: 20
body: 8
6Variable
7ExprTuple9
8Operationoperator: 10
operands: 11
9ExprRangelambda_map: 12
start_index: 13
end_index: 14
10Literal
11ExprTuple16, 15
12Lambdaparameter: 20
body: 16
13Literal
14Variable
15IndexedVarvariable: 17
index: 20
16IndexedVarvariable: 18
index: 20
17Variable
18Variable
19ExprTuple20
20Variable