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, C, Lambda
from proveit.logic import Boolean, Forall, Implies, Not

# build up the expression from sub-expressions
expr = Lambda(C, Forall(instance_param_or_params = [A], instance_expr = C, domain = Boolean, conditions = [Implies(A, C), Implies(Not(A), C)]))

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())

C \mapsto \left[\forall_{A \in \mathbb{B}~|~A \Rightarrow C, (\lnot A) \Rightarrow C}~C\right]

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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