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Expression of type And

from the theory of proveit.numbers.multiplication

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, Variable, a, b, i, j, x, y
from proveit.logic import And, InSet
from proveit.numbers import Complex, 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), Complex), one, i), InSet(x, Complex), InSet(y, Complex), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Complex), one, j))
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{C}\right) \land  \left(a_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(a_{i} \in \mathbb{C}\right) \land \left(x \in \mathbb{C}\right) \land \left(y \in \mathbb{C}\right)\land \left(b_{1} \in \mathbb{C}\right) \land  \left(b_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(b_{j} \in \mathbb{C}\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: 12
end_index: 8
4Operationoperator: 19
operands: 9
5Operationoperator: 19
operands: 10
6ExprRangelambda_map: 11
start_index: 12
end_index: 13
7Lambdaparameter: 27
body: 14
8Variable
9ExprTuple15, 23
10ExprTuple16, 23
11Lambdaparameter: 27
body: 17
12Literal
13Variable
14Operationoperator: 19
operands: 18
15Variable
16Variable
17Operationoperator: 19
operands: 20
18ExprTuple21, 23
19Literal
20ExprTuple22, 23
21IndexedVarvariable: 24
index: 27
22IndexedVarvariable: 25
index: 27
23Literal
24Variable
25Variable
26ExprTuple27
27Variable