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Proof step 32 from proof path-equiv-reach (previous step)

(a ' + y0) .last = y .butlast .last, # y = 1 + # y0, reach(a, y .butlast .last, # y0), path(a ' + y), path(a ' + y0) ⊦ y = [], ∃ c. reach(a, c, # y0) ∧ y .last ∈ succ(c)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 31:
y = y1 + a0 ', (a ' + y0) .last = y1 .last, # y = 1 + # y0, reach(a, y1 .last, # y0), path(a ' + y), path(a ' + y0) ⊦ y = [], ∃ c. reach(a, c, # y0) ∧ a0 ∈ succ(c)

Rule argument

[x0lemmaarg: spec-name: list-last instance-name: lemma-name: last-elim antecedent: x ≠ [] succedent: a = x .last ∧ y = x .butlast ↔ x = y + a ' substlist: [x, a, y] → [y, a0, y1] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : x ≠ [] ⊦ a = x .last ∧ y = x .butlast ↔ x = y + a '])], [EXTRATERMS : (y, a0, y1)]]