# 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, 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 = 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())

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..

In [5]:
stored_expr.style_options()

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

core typesub-expressionsexpression
0Lambdaparameter: 14
body: 2
1ExprTuple14
2Conditionalvalue: 3
condition: 4
3Operationoperator: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8
6Literal
7ExprTuple14, 9
8ExprRangelambda_map: 10
start_index: 15
end_index: 20
9Operationoperator: 11
operands: 12
10Lambdaparameter: 17
body: 14
11Literal
12ExprTuple15, 16
13ExprTuple17
14Variable
15Variable
16Operationoperator: 18
operands: 19
17Variable
18Literal
19ExprTuple20, 21
20Variable
21Literal