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Proof step 6 from proof diff-wfrec (previous step)

∀ a, y. x0 \ (a ' + y) = (x0 -l a) \ y, a0 = a ∨ a0 ∈ y ⊦ x0 \ (a ' + y) = ((a0 ' + x0) -l a) \ y

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ a ≠ b → (b ' + x) -l a = b ' + (x -l a)
Proof step 8:
¬ a ≠ a0, ∀ a, y. x0 \ (a ' + y) = (x0 -l a) \ y, a0 = a ∨ a0 ∈ y ⊦ x0 \ (a ' + y) = ((a0 ' + x0) -l a) \ y
Proof step 10:
a ≠ a0, ∀ a, y. x0 \ (a ' + y) = (x0 -l a) \ y, a0 = a ∨ a0 ∈ y ⊦ x0 \ (a ' + y) = (a0 ' + (x0 -l a)) \ y

Rule argument

spec: list-del inst: name: del-n seq: ⊦ a ≠ b → (b ' + x) -l a = b ' + (x -l a) subst: [a, x, b] → [a, x0, a0] flags: rewrite

Additional information

Used terms: a, x0, a0