Expression of type Lambda

from the theory of proveit.logic.sets.functions

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 Forall, Functions, InSet

# build up the expression from sub-expressions
expr = Lambda(f, Conditional(InSet(f, Functions(A, B)), Forall(instance_param_or_params = [x], instance_expr = InSet(fx, B), domain = A)))

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 \rightarrow B\right] \textrm{ if } \forall_{x \in A}~\left(f\left(x\right) \in 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: 21 body: 2
1	ExprTuple	21
2	Conditional	value: 3 condition: 4
3	Operation	operator: 16 operands: 5
4	Operation	operator: 6 operand: 9
5	ExprTuple	21, 8
6	Literal
7	ExprTuple	9
8	Operation	operator: 10 operands: 11
9	Lambda	parameter: 23 body: 12
10	Literal
11	ExprTuple	20, 19
12	Conditional	value: 13 condition: 14
13	Operation	operator: 16 operands: 15
14	Operation	operator: 16 operands: 17
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	23, 20
18	Operation	operator: 21 operand: 23
19	Variable
20	Variable
21	Variable
22	ExprTuple	23
23	Variable