# from the theory of proveit.logic.booleans.conjunction¶

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 A, Conditional, ExprRange, ExprTuple, Lambda, Variable, i, j
from proveit.logic import And
from proveit.numbers import Add, LessEq, one

In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(A, Conditional(And(ExprRange(Variable("_a", latex_format = r"{_{-}a}"), A, i, j)), And(A, LessEq(i, Add(j, one))))))

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 \mapsto \left\{A \land  A \land  ..\left(j - i - 2\right) \times.. \land  A \textrm{ if } A ,  i \leq \left(j + 1\right)\right..\right)

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0ExprTuple1
1Lambdaparameter: 15
body: 3
2ExprTuple15
3Conditionalvalue: 4
condition: 5
4Operationoperator: 7
operands: 6
5Operationoperator: 7
operands: 8
6ExprTuple9
7Literal
8ExprTuple15, 10
9ExprRangelambda_map: 11
start_index: 16
end_index: 21
10Operationoperator: 12
operands: 13
11Lambdaparameter: 18
body: 15
12Literal
13ExprTuple16, 17
14ExprTuple18
15Variable
16Variable
17Operationoperator: 19
operands: 20
18Variable
19Literal
20ExprTuple21, 22
21Variable
22Literal