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Expression of type Lambda

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, Lambda, f
from proveit.logic import And, Bijections, InSet, Injections, Surjections
In [2]:
# build up the expression from sub-expressions
expr = 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())
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..
In [5]:
stored_expr.style_options()
no style options
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Lambdaparameter: 16
body: 2
1ExprTuple16
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operands: 6
4Operationoperator: 12
operands: 7
5Literal
6ExprTuple8, 9
7ExprTuple16, 10
8Operationoperator: 12
operands: 11
9Operationoperator: 12
operands: 13
10Operationoperator: 14
operands: 20
11ExprTuple16, 15
12Literal
13ExprTuple16, 17
14Literal
15Operationoperator: 18
operands: 20
16Variable
17Operationoperator: 19
operands: 20
18Literal
19Literal
20ExprTuple21, 22
21Variable
22Variable