# from the theory of proveit.numbers.addition.subtraction¶

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, e, i, j, k
from proveit.logic import And, Equals, 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(b, Complex), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), Complex), one, j), InSet(d, Complex), ExprRange(sub_expr1, InSet(IndexedVar(e, sub_expr1), Complex), one, k), Equals(b, d))

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 \in \mathbb{C}\right)\land \left(c_{1} \in \mathbb{C}\right) \land  \left(c_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(c_{j} \in \mathbb{C}\right) \land \left(d \in \mathbb{C}\right)\land \left(e_{1} \in \mathbb{C}\right) \land  \left(e_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(e_{k} \in \mathbb{C}\right) \land \left(b = d\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, 7, 8
3ExprRangelambda_map: 9
start_index: 16
end_index: 10
4Operationoperator: 27
operands: 11
5ExprRangelambda_map: 12
start_index: 16
end_index: 13
6Operationoperator: 27
operands: 14
7ExprRangelambda_map: 15
start_index: 16
end_index: 17
8Operationoperator: 18
operands: 19
9Lambdaparameter: 37
body: 20
10Variable
11ExprTuple23, 32
12Lambdaparameter: 37
body: 21
13Variable
14ExprTuple24, 32
15Lambdaparameter: 37
body: 22
16Literal
17Variable
18Literal
19ExprTuple23, 24
20Operationoperator: 27
operands: 25
21Operationoperator: 27
operands: 26
22Operationoperator: 27
operands: 28
23Variable
24Variable
25ExprTuple29, 32
26ExprTuple30, 32
27Literal
28ExprTuple31, 32
29IndexedVarvariable: 33
index: 37
30IndexedVarvariable: 34
index: 37
31IndexedVarvariable: 35
index: 37
32Literal
33Variable
34Variable
35Variable
36ExprTuple37
37Variable