Expression of type Lambda

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

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

# 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:

# 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

# 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..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 15 body: 2
1	ExprTuple	15
2	Conditional	value: 3 condition: 4
3	Operation	operator: 17 operands: 5
4	Operation	operator: 17 operands: 6
5	ExprTuple	15, 8
6	ExprTuple	7, 8
7	Lambda	parameter: 19 body: 9
8	Operation	operator: 10 operands: 11
9	Conditional	value: 12 condition: 13
10	Literal
11	ExprTuple	20, 14
12	Operation	operator: 15 operand: 19
13	Operation	operator: 17 operands: 18
14	Variable
15	Variable
16	ExprTuple	19
17	Literal
18	ExprTuple	19, 20
19	Variable
20	Variable