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

# build up the expression from sub-expressions
expr = Lambda(P, Implies(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(\left[\forall_{A \in \mathbb{B}}~P\left(A\right)\right] \Rightarrow \left(P\left(\top\right) \land P\left(\bot\right)\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: 21 body: 2
1	ExprTuple	21
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 7 operand: 11
6	Operation	operator: 9 operands: 10
7	Literal
8	ExprTuple	11
9	Literal
10	ExprTuple	12, 13
11	Lambda	parameter: 25 body: 14
12	Operation	operator: 21 operand: 19
13	Operation	operator: 21 operand: 20
14	Conditional	value: 17 condition: 18
15	ExprTuple	19
16	ExprTuple	20
17	Operation	operator: 21 operand: 25
18	Operation	operator: 23 operands: 24
19	Literal
20	Literal
21	Variable
22	ExprTuple	25
23	Literal
24	ExprTuple	25, 26
25	Variable
26	Literal