# 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.
# import Expression classes needed to build the expression
from proveit import ExprRange, IndexedVar, Variable, a, n
from proveit.logic import And, InSet
from proveit.numbers import RationalNonNeg, 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), RationalNonNeg), one, 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(a_{1} \in \mathbb{Q}^{\geq 0}\right) \land  \left(a_{2} \in \mathbb{Q}^{\geq 0}\right) \land  \ldots \land  \left(a_{n} \in \mathbb{Q}^{\geq 0}\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
3ExprRangelambda_map: 4
start_index: 5
end_index: 6
4Lambdaparameter: 14
body: 7
5Literal
6Variable
7Operationoperator: 8
operands: 9
8Literal
9ExprTuple10, 11
10IndexedVarvariable: 12
index: 14
11Literal
12Variable
13ExprTuple14
14Variable