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, Q, QofA
from proveit.logic import And, Boolean, Forall, QimplPofFalse, QimplPofTrue

# build up the expression from sub-expressions
expr = Lambda([P, Q], Conditional(Forall(instance_param_or_params = [A], instance_expr = PofA, domain = Boolean, condition = QofA), And(QimplPofTrue, QimplPofFalse)))

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())

\left(P, Q\right) \mapsto \left\{\forall_{A \in \mathbb{B}~|~Q\left(A\right)}~P\left(A\right) \textrm{ if } Q\left(\top\right) \Rightarrow P\left(\top\right) ,  Q\left(\bot\right) \Rightarrow 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	parameters: 1 body: 2
1	ExprTuple	24, 32
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 21 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameter: 35 body: 11
9	Operation	operator: 13 operands: 12
10	Operation	operator: 13 operands: 14
11	Conditional	value: 15 condition: 16
12	ExprTuple	17, 18
13	Literal
14	ExprTuple	19, 20
15	Operation	operator: 24 operand: 35
16	Operation	operator: 21 operands: 22
17	Operation	operator: 32 operand: 28
18	Operation	operator: 24 operand: 28
19	Operation	operator: 32 operand: 29
20	Operation	operator: 24 operand: 29
21	Literal
22	ExprTuple	26, 27
23	ExprTuple	28
24	Variable
25	ExprTuple	29
26	Operation	operator: 30 operands: 31
27	Operation	operator: 32 operand: 35
28	Literal
29	Literal
30	Literal
31	ExprTuple	35, 34
32	Variable
33	ExprTuple	35
34	Literal
35	Variable