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Proof step 17 from proof eq-01 (previous step)

x1 + a ' + b ' + y + c ' + z = (y0 + a ' + c ') + z0, ∀ a, b, y, c, z, x0, z0. x1 + a ' + b ' + y + c ' + z = x0 + a ' + c ' + z0 → b = c ∨ a = b ∨ a = c ∨ a ∈ y ∨ a ∈ x1 ∨ a ∈ z ∨ c ∈ x1 ∨ c ∈ z ∨ dups(x1 + z) ⊦ a = c, a = b, b = c, c = a0, a = a0, c ∈ z, c ∈ x1, a ∈ z, a ∈ x1, a ∈ y, dups(x1 + z), a0 ∈ z, a0 ∈ x1

User applied rule all left

And closed the goal!

Rule argument

pos: left 2 terms: a, b, y, c, z, y0, z0 abort: F discard: T computed: T

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: a, b, y, c, z, y0, z0