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, Conditional, Lambda, P, PofA
from proveit.logic import And, Boolean, Forall, PofFalse, PofTrue

# build up the expression from sub-expressions
expr = Lambda(P, Conditional(Forall(instance_param_or_params = [A], instance_expr = PofA, domain = Boolean), And(PofTrue, PofFalse)))

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())

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

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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