logo

Expression of type ExprTuple

from the theory of proveit.logic.sets.functions.bijections

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 A, Conditional, ExprTuple, Lambda, fx, fy, x, y
from proveit.logic import And, InSet, NotEquals
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda([x, y], Conditional(NotEquals(fx, fy), And(InSet(x, A), InSet(y, A), NotEquals(x, y)))))
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(\left(x, y\right) \mapsto \left\{f\left(x\right) \neq f\left(y\right) \textrm{ if } x \in A ,  y \in A ,  x \neq y\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
1Lambdaparameters: 20
body: 2
2Conditionalvalue: 3
condition: 4
3Operationoperator: 19
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple10, 11, 12
8Operationoperator: 14
operand: 22
9Operationoperator: 14
operand: 23
10Operationoperator: 17
operands: 16
11Operationoperator: 17
operands: 18
12Operationoperator: 19
operands: 20
13ExprTuple22
14Variable
15ExprTuple23
16ExprTuple22, 21
17Literal
18ExprTuple23, 21
19Literal
20ExprTuple22, 23
21Variable
22Variable
23Variable