Algebra.op_four_sym: law of bend-mathlib@0.8.1.0 Import: import bend-mathlib@0.8.1.0/algebra.bend as Algebra Lines 336-346 of bend-mathlib@0.8.1.0/algebra.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/algebra.bend&start_line=336&end_line=346 import Base # Middle-four interchange from associativity and commutativity, reversed to rewrite toward the simple side. law op_four_sym: for ~A: Data for ~op: A -> A -> A for ~assoc: @x: A -> @y: A -> @z: A -> {op(op(x, y), z) == op(x, op(y, z)) : A} for ~comm: @x: A -> @y: A -> {op(x, y) == op(y, x) : A} for +a: A for +b: A for +c: A for +d: A {op(op(a, c), op(b, d)) == op(op(a, b), op(c, d)) : A} Uses (2): https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/algebra.bend&name=op_four