# from the theory of proveit.core_expr_types.conditionals¶

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 Conditional, Lambda, a
from proveit.core_expr_types import Q_1_to_m, R_1_to_n
from proveit.logic import And, Equals, TRUE

In [2]:
# build up the expression from sub-expressions
expr = Lambda([a, Q_1_to_m, R_1_to_n], Equals(Conditional(a, And(Q_1_to_m, TRUE, R_1_to_n)), Conditional(a, And(Q_1_to_m, R_1_to_n))).with_wrapping_at(1))

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, Q_{1}, Q_{2}, \ldots, Q_{m}, R_{1}, R_{2}, \ldots, R_{n}\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \left\{a \textrm{ if } Q_{1} ,  Q_{2} ,  \ldots ,  Q_{m} ,  \top, R_{1} ,  R_{2} ,  \ldots ,  R_{n}\right.. \\  = \left\{a \textrm{ if } Q_{1} ,  Q_{2} ,  \ldots ,  Q_{m}, R_{1} ,  R_{2} ,  \ldots ,  R_{n}\right.. \end{array} \end{array}\right)

In [5]:
stored_expr.style_options()

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

core typesub-expressionsexpression
0Lambdaparameters: 1
body: 2
1ExprTuple8, 14, 15
2Operationoperator: 3
operands: 4
3Literal
4ExprTuple5, 6
5Conditionalvalue: 8
condition: 7
6Conditionalvalue: 8
condition: 9
7Operationoperator: 11
operands: 10
8Variable
9Operationoperator: 11
operands: 12
10ExprTuple14, 13, 15
11Literal
12ExprTuple14, 15
13Literal
14ExprRangelambda_map: 16
start_index: 19
end_index: 17
15ExprRangelambda_map: 18
start_index: 19
end_index: 20
16Lambdaparameter: 26
body: 21
17Variable
18Lambdaparameter: 26
body: 22
19Literal
20Variable
21IndexedVarvariable: 23
index: 26
22IndexedVarvariable: 24
index: 26
23Variable
24Variable
25ExprTuple26
26Variable