Expression of type Lambda

from the theory of proveit.logic.booleans.disjunction

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, B, C, Conditional, Lambda
from proveit.logic import And, Boolean, Forall, Implies, InSet, Or

# build up the expression from sub-expressions
expr = Lambda([A, B], Conditional(Forall(instance_param_or_params = [C], instance_expr = C, conditions = [Implies(A, C), Implies(B, C)]), And(InSet(A, Boolean), InSet(B, Boolean), Or(A, B))))

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(A, B\right) \mapsto \left\{\forall_{C~|~A \Rightarrow C, B \Rightarrow C}~C \textrm{ if } A \in \mathbb{B} ,  B \in \mathbb{B} ,  A \lor B\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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