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Proof step 19 from proof last-elim (previous step)

∀ a2, y0. a2 = ((a0 ' + y) + a ').last ∧ y0 = ((a0 ' + y) + a ').butlast ↔ (a0 ' + y) + a ' = y0 + a2 ' ⊦ a = ((a0 ' + y) + a ').last ∧ a0 ' + y = ((a0 ' + y) + a ').butlast

User applied rule all left

And closed the goal!

Rule argument

pos: left 1 terms: a, a0 ' + y abort: F discard: T computed: T

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: a, a0 ' + y