# from the theory of proveit.numbers.addition¶

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 ExprRange, IndexedVar, Variable, a, b, c, d, i, j, k
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), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), Complex), one, j), InSet(c, Complex), ExprRange(sub_expr1, InSet(IndexedVar(d, sub_expr1), Complex), one, k))

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(b_{1} \in \mathbb{C}\right) \land  \left(b_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(b_{j} \in \mathbb{C}\right) \land \left(c \in \mathbb{C}\right)\land \left(d_{1} \in \mathbb{C}\right) \land  \left(d_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(d_{k} \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: 13
end_index: 8
4ExprRangelambda_map: 9
start_index: 13
end_index: 10
5Operationoperator: 21
operands: 11
6ExprRangelambda_map: 12
start_index: 13
end_index: 14
7Lambdaparameter: 31
body: 15
8Variable
9Lambdaparameter: 31
body: 16
10Variable
11ExprTuple17, 26
12Lambdaparameter: 31
body: 18
13Literal
14Variable
15Operationoperator: 21
operands: 19
16Operationoperator: 21
operands: 20
17Variable
18Operationoperator: 21
operands: 22
19ExprTuple23, 26
20ExprTuple24, 26
21Literal
22ExprTuple25, 26
23IndexedVarvariable: 27
index: 31
24IndexedVarvariable: 28
index: 31
25IndexedVarvariable: 29
index: 31
26Literal
27Variable
28Variable
29Variable
30ExprTuple31
31Variable