Expression of type Forall

from the theory of proveit.logic.sets.functions.bijections

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 Bijections, Forall, InSet

# build up the expression from sub-expressions
sub_expr1 = Bijections(A, B)
expr = Forall(instance_param_or_params = [A, B], instance_expr = Forall(instance_param_or_params = [f], instance_expr = InSet(f, sub_expr1), condition = InSet(Lambda(x, Conditional(fx, InSet(x, A))), sub_expr1)))

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_{A, B}~\left[\forall_{f~|~\left[x \mapsto \left\{f\left(x\right) \textrm{ if } x \in A\right..\right] \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} B\right]}~\left(f \in \left[A \xrightarrow[\text{onto}]{\text{1-to-1}} 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: 4 operand: 2
1	ExprTuple	2
2	Lambda	parameters: 17 body: 3
3	Operation	operator: 4 operand: 6
4	Literal
5	ExprTuple	6
6	Lambda	parameter: 21 body: 8
7	ExprTuple	21
8	Conditional	value: 9 condition: 10
9	Operation	operator: 23 operands: 11
10	Operation	operator: 23 operands: 12
11	ExprTuple	21, 14
12	ExprTuple	13, 14
13	Lambda	parameter: 25 body: 15
14	Operation	operator: 16 operands: 17
15	Conditional	value: 18 condition: 19
16	Literal
17	ExprTuple	26, 20
18	Operation	operator: 21 operand: 25
19	Operation	operator: 23 operands: 24
20	Variable
21	Variable
22	ExprTuple	25
23	Literal
24	ExprTuple	25, 26
25	Variable
26	Variable