Expression of type Forall

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

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

\forall_{f, A, B}~\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()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 10 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 3 body: 4
3	ExprTuple	25, 24, 23
4	Operation	operator: 5 operands: 6
5	Literal
6	ExprTuple	7, 8
7	Operation	operator: 20 operands: 9
8	Operation	operator: 10 operand: 13
9	ExprTuple	25, 12
10	Literal
11	ExprTuple	13
12	Operation	operator: 14 operands: 15
13	Lambda	parameter: 27 body: 16
14	Literal
15	ExprTuple	24, 23
16	Conditional	value: 17 condition: 18
17	Operation	operator: 20 operands: 19
18	Operation	operator: 20 operands: 21
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	27, 24
22	Operation	operator: 25 operand: 27
23	Variable
24	Variable
25	Variable
26	ExprTuple	27
27	Variable