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, Equals, Forall, PofFalse, PofTrue, TRUE

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

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] = \top \textrm{ if } P\left(\top\right) = \top ,  P\left(\bot\right) = \top\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 26 body: 2
1	ExprTuple	26
2	Conditional	value: 3 condition: 4
3	Operation	operator: 14 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 24
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 11 operand: 16
9	Operation	operator: 14 operands: 13
10	Operation	operator: 14 operands: 15
11	Literal
12	ExprTuple	16
13	ExprTuple	17, 24
14	Literal
15	ExprTuple	18, 24
16	Lambda	parameter: 30 body: 19
17	Operation	operator: 26 operand: 24
18	Operation	operator: 26 operand: 25
19	Conditional	value: 22 condition: 23
20	ExprTuple	24
21	ExprTuple	25
22	Operation	operator: 26 operand: 30
23	Operation	operator: 28 operands: 29
24	Literal
25	Literal
26	Variable
27	ExprTuple	30
28	Literal
29	ExprTuple	30, 31
30	Variable
31	Literal