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, Lambda, f, fx, x
from proveit.logic import Forall, Functions, InSet

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

\left(A, B\right) \mapsto \left[\forall_{f~|~\forall_{x \in A}~\left(f\left(x\right) \in B\right)}~\left(f \in \left[A \rightarrow B\right]\right)\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 14 body: 1
1	Operation	operator: 9 operand: 3
2	ExprTuple	3
3	Lambda	parameter: 24 body: 5
4	ExprTuple	24
5	Conditional	value: 6 condition: 7
6	Operation	operator: 19 operands: 8
7	Operation	operator: 9 operand: 12
8	ExprTuple	24, 11
9	Literal
10	ExprTuple	12
11	Operation	operator: 13 operands: 14
12	Lambda	parameter: 26 body: 15
13	Literal
14	ExprTuple	23, 22
15	Conditional	value: 16 condition: 17
16	Operation	operator: 19 operands: 18
17	Operation	operator: 19 operands: 20
18	ExprTuple	21, 22
19	Literal
20	ExprTuple	26, 23
21	Operation	operator: 24 operand: 26
22	Variable
23	Variable
24	Variable
25	ExprTuple	26
26	Variable