Expression of type Forall

from the theory of proveit.linear_algebra.linear_maps

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 Conditional, Lambda, V, x
from proveit.linear_algebra import Identity
from proveit.logic import Equals, Forall, InSet

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [V], instance_expr = Equals(Identity(V), Lambda(x, Conditional(x, InSet(x, V)))))

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_{V}~\left(I_{V} = \left[x \mapsto \left\{x \textrm{ if } x \in V\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: 1 operand: 3
1	Literal
2	ExprTuple	3
3	Lambda	parameter: 17 body: 4
4	Operation	operator: 5 operands: 6
5	Literal
6	ExprTuple	7, 8
7	Operation	operator: 9 operand: 17
8	Lambda	parameter: 16 body: 12
9	Literal
10	ExprTuple	17
11	ExprTuple	16
12	Conditional	value: 16 condition: 13
13	Operation	operator: 14 operands: 15
14	Literal
15	ExprTuple	16, 17
16	Variable
17	Variable