Expression of type Lambda

from the theory of proveit.logic.booleans

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, Function, Lambda, P
from proveit.logic import Boolean, Forall, InSet

# build up the expression from sub-expressions
expr = Lambda(A, Conditional(Forall(instance_param_or_params = [B], instance_expr = Function(P, [A, B]), domain = Boolean), InSet(A, Boolean)))

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())

A \mapsto \left\{\forall_{B \in \mathbb{B}}~P\left(A, B\right) \textrm{ if } A \in \mathbb{B}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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