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, Equals, FALSE, Forall, Implies, PofFalse, PofTrue, TRUE

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

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(\left(P\left(\top\right) = \bot\right) \land \left(P\left(\bot\right) = \top\right)\right) \Rightarrow \left(\left[\forall_{A \in \mathbb{B}}~P\left(A\right)\right] = \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: 28 body: 2
1	ExprTuple	28
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Operation	operator: 7 operands: 8
6	Operation	operator: 14 operands: 9
7	Literal
8	ExprTuple	10, 11
9	ExprTuple	12, 25
10	Operation	operator: 14 operands: 13
11	Operation	operator: 14 operands: 15
12	Operation	operator: 16 operand: 20
13	ExprTuple	18, 25
14	Literal
15	ExprTuple	19, 24
16	Literal
17	ExprTuple	20
18	Operation	operator: 28 operand: 24
19	Operation	operator: 28 operand: 25
20	Lambda	parameter: 32 body: 23
21	ExprTuple	24
22	ExprTuple	25
23	Conditional	value: 26 condition: 27
24	Literal
25	Literal
26	Operation	operator: 28 operand: 32
27	Operation	operator: 30 operands: 31
28	Variable
29	ExprTuple	32
30	Literal
31	ExprTuple	32, 33
32	Variable
33	Literal