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 Equals, Forall, Functions, InSet

# build up the expression from sub-expressions
expr = Lambda([f, A, B], Equals(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())

\left(f, A, B\right) \mapsto \left(\left(f \in \left[A \rightarrow B\right]\right) = \left[\forall_{x \in A}~\left(f\left(x\right) \in 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: 1 body: 2
1	ExprTuple	23, 22, 21
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 18 operands: 7
6	Operation	operator: 8 operand: 11
7	ExprTuple	23, 10
8	Literal
9	ExprTuple	11
10	Operation	operator: 12 operands: 13
11	Lambda	parameter: 25 body: 14
12	Literal
13	ExprTuple	22, 21
14	Conditional	value: 15 condition: 16
15	Operation	operator: 18 operands: 17
16	Operation	operator: 18 operands: 19
17	ExprTuple	20, 21
18	Literal
19	ExprTuple	25, 22
20	Operation	operator: 23 operand: 25
21	Variable
22	Variable
23	Variable
24	ExprTuple	25
25	Variable