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Expression of type And

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.
%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, c, i, j
from proveit.logic import And, InSet
from proveit.numbers import Less, RationalNonPos, one, zero
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), RationalNonPos), one, i), InSet(b, RationalNonPos), ExprRange(sub_expr1, InSet(IndexedVar(c, sub_expr1), RationalNonPos), one, j), Less(b, zero))
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}^{\leq 0}\right) \land  \left(a_{2} \in \mathbb{Q}^{\leq 0}\right) \land  \ldots \land  \left(a_{i} \in \mathbb{Q}^{\leq 0}\right) \land \left(b \in \mathbb{Q}^{\leq 0}\right)\land \left(c_{1} \in \mathbb{Q}^{\leq 0}\right) \land  \left(c_{2} \in \mathbb{Q}^{\leq 0}\right) \land  \ldots \land  \left(c_{j} \in \mathbb{Q}^{\leq 0}\right) \land \left(b < 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, 4, 5, 6
3ExprRangelambda_map: 7
start_index: 11
end_index: 8
4Operationoperator: 20
operands: 9
5ExprRangelambda_map: 10
start_index: 11
end_index: 12
6Operationoperator: 13
operands: 14
7Lambdaparameter: 28
body: 15
8Variable
9ExprTuple17, 24
10Lambdaparameter: 28
body: 16
11Literal
12Variable
13Literal
14ExprTuple17, 18
15Operationoperator: 20
operands: 19
16Operationoperator: 20
operands: 21
17Variable
18Literal
19ExprTuple22, 24
20Literal
21ExprTuple23, 24
22IndexedVarvariable: 25
index: 28
23IndexedVarvariable: 26
index: 28
24Literal
25Variable
26Variable
27ExprTuple28
28Variable