Expression of type ExprTuple

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

# build up the expression from sub-expressions
expr = ExprTuple(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())

\left(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..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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