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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, fx, x
from proveit.logic import Bijections, InSet
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Bijections(A, B)
expr = Lambda(f, Conditional(InSet(f, sub_expr1), InSet(Lambda(x, Conditional(fx, InSet(x, A))), sub_expr1)))
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\{f \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} B\right] \textrm{ if } \left[x \mapsto \left\{f\left(x\right) \textrm{ if } x \in A\right..\right] \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: 15
body: 2
1ExprTuple15
2Conditionalvalue: 3
condition: 4
3Operationoperator: 17
operands: 5
4Operationoperator: 17
operands: 6
5ExprTuple15, 8
6ExprTuple7, 8
7Lambdaparameter: 19
body: 9
8Operationoperator: 10
operands: 11
9Conditionalvalue: 12
condition: 13
10Literal
11ExprTuple20, 14
12Operationoperator: 15
operand: 19
13Operationoperator: 17
operands: 18
14Variable
15Variable
16ExprTuple19
17Literal
18ExprTuple19, 20
19Variable
20Variable