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, C, Conditional, ExprRange, IndexedVar, Lambda, Variable, m
from proveit.core_expr_types import A_1_to_m
from proveit.logic import Boolean, Forall, Implies, InSet, Or
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda(m, Conditional(Forall(instance_param_or_params = [A_1_to_m], instance_expr = Forall(instance_param_or_params = [C], instance_expr = C, condition = ExprRange(sub_expr1, Implies(IndexedVar(A, sub_expr1), C), one, m)), domain = Boolean, condition = Or(A_1_to_m)), InSet(m, Natural)))

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())

m \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{m} \in \mathbb{B}~|~A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m}}~\left[\forall_{C~|~\left(A_{1} \Rightarrow C\right), \left(A_{2} \Rightarrow C\right), \ldots, \left(A_{m} \Rightarrow C\right)}~C\right] \textrm{ if } m \in \mathbb{N}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 35 body: 2
1	ExprTuple	35
2	Conditional	value: 3 condition: 4
3	Operation	operator: 12 operand: 7
4	Operation	operator: 28 operands: 6
5	ExprTuple	7
6	ExprTuple	35, 8
7	Lambda	parameters: 22 body: 9
8	Literal
9	Conditional	value: 10 condition: 11
10	Operation	operator: 12 operand: 15
11	Operation	operator: 26 operands: 14
12	Literal
13	ExprTuple	15
14	ExprTuple	16, 17
15	Lambda	parameter: 40 body: 19
16	ExprRange	lambda_map: 20 start_index: 34 end_index: 35
17	Operation	operator: 21 operands: 22
18	ExprTuple	40
19	Conditional	value: 40 condition: 23
20	Lambda	parameter: 43 body: 24
21	Literal
22	ExprTuple	25
23	Operation	operator: 26 operands: 27
24	Operation	operator: 28 operands: 29
25	ExprRange	lambda_map: 30 start_index: 34 end_index: 35
26	Literal
27	ExprTuple	31
28	Literal
29	ExprTuple	39, 32
30	Lambda	parameter: 43 body: 39
31	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
32	Literal
33	Lambda	parameter: 43 body: 36
34	Literal
35	Variable
36	Operation	operator: 37 operands: 38
37	Literal
38	ExprTuple	39, 40
39	IndexedVar	variable: 41 index: 43
40	Variable
41	Variable
42	ExprTuple	43
43	Variable