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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 Less, RealPos, 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), RealPos), one, i), ExprRange(sub_expr1, InSet(IndexedVar(b, sub_expr1), RealPos), one, j), Less(x, y))
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{R}^+\right) \land  \left(a_{2} \in \mathbb{R}^+\right) \land  \ldots \land  \left(a_{i} \in \mathbb{R}^+\right)\land \left(b_{1} \in \mathbb{R}^+\right) \land  \left(b_{2} \in \mathbb{R}^+\right) \land  \ldots \land  \left(b_{j} \in \mathbb{R}^+\right) \land \left(x < y\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
3ExprRangelambda_map: 6
start_index: 9
end_index: 7
4ExprRangelambda_map: 8
start_index: 9
end_index: 10
5Operationoperator: 11
operands: 12
6Lambdaparameter: 26
body: 13
7Variable
8Lambdaparameter: 26
body: 14
9Literal
10Variable
11Literal
12ExprTuple15, 16
13Operationoperator: 18
operands: 17
14Operationoperator: 18
operands: 19
15Variable
16Variable
17ExprTuple20, 22
18Literal
19ExprTuple21, 22
20IndexedVarvariable: 23
index: 26
21IndexedVarvariable: 24
index: 26
22Literal
23Variable
24Variable
25ExprTuple26
26Variable