Expression of type Forall

from the theory of proveit.core_expr_types.lambda_maps

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 Composition, Function, Lambda, f, fx, g, gy, gz, x, y, z
from proveit.logic import Equals, Forall

# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [f, g], instance_expr = Equals(Composition(Lambda(x, fx), Lambda(y, gy)), Lambda(z, Function(f, [gz]))))

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())

\forall_{f, g}~\left(\left(\left[x \mapsto f\left(x\right)\right] \circ \left[y \mapsto g\left(y\right)\right]\right) = \left[z \mapsto f\left(g\left(z\right)\right)\right]\right)

stored_expr.style_options()

name	description	default	current value	related methods
with_wrapping	If 'True', wrap the Expression after the parameters	None	None/False	('with_wrapping',)
condition_wrapping	Wrap 'before' or 'after' the condition (or None).	None	None/False	('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_params	If 'True', wraps every two parameters AND wraps the Expression after the parameters	None	None/False	('with_params',)
justification	justify to the 'left', 'center', or 'right' in the array cells	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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