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, B, Conditional, ExprTuple, Lambda, f
from proveit.logic import And, Bijections, InSet, Injections, Surjections
In [2]:
# build up the expression from sub-expressions
expr = ExprTuple(Lambda(f, Conditional(And(InSet(f, Injections(A, B)), InSet(f, Surjections(A, B))), InSet(f, Bijections(A, B)))))
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(f \mapsto \left\{\left(f \in \left[A \xrightarrow[]{\text{1-to-1}} B\right]\right) \land \left(f \in \left[A \xrightarrow[\text{onto}]{} B\right]\right) \textrm{ if } f \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} B\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: 17
body: 3
2ExprTuple17
3Conditionalvalue: 4
condition: 5
4Operationoperator: 6
operands: 7
5Operationoperator: 13
operands: 8
6Literal
7ExprTuple9, 10
8ExprTuple17, 11
9Operationoperator: 13
operands: 12
10Operationoperator: 13
operands: 14
11Operationoperator: 15
operands: 21
12ExprTuple17, 16
13Literal
14ExprTuple17, 18
15Literal
16Operationoperator: 19
operands: 21
17Variable
18Operationoperator: 20
operands: 21
19Literal
20Literal
21ExprTuple22, 23
22Variable
23Variable