# from the theory of proveit.logic.equality¶

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, b, c, d
from proveit.logic import And, Equals

In [2]:
# build up the expression from sub-expressions
expr = Lambda([a, b, c, d], Conditional(Equals(a, d), And(Equals(a, b), Equals(b, c), Equals(c, d))))

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, b, c, d\right) \mapsto \left\{a = d \textrm{ if } a = b ,  b = c ,  c = d\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
1ExprTuple15, 16, 17, 18
2Conditionalvalue: 3
condition: 4
3Operationoperator: 13
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple15, 18
6Literal
7ExprTuple8, 9, 10
8Operationoperator: 13
operands: 11
9Operationoperator: 13
operands: 12
10Operationoperator: 13
operands: 14
11ExprTuple15, 16
12ExprTuple16, 17
13Literal
14ExprTuple17, 18
15Variable
16Variable
17Variable
18Variable