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Proof step 4 from proof fits-rec (previous step)

⊦ sks = [], fits(r, sks, st) ↔ r ≠ jvmref ∧ is_referencevalue(st[r -- sks .first]) ∧ (is_classtype(st[r -- _type] .type) → sks .first ∈ instfields(st[r -- _type] .type .class)) ∧ (is_arraytype(st[r -- _type] .type) → ¬ is_fskey(sks .first) ∧ ¬ sks .first .index < 0 ∧ ¬ st[r -- _length] .intval ≤ sks .first .index) ∧ fits(st[r -- sks .first] .refval, sks .rest, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 3:
sks = sk + sks0 ⊦ sks = [], fits(r, sks, st) ↔ r ≠ jvmref ∧ is_referencevalue(st[r -- sk]) ∧ (is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class)) ∧ (is_arraytype(st[r -- _type] .type) → ¬ is_fskey(sk) ∧ ¬ sk .index < 0 ∧ ¬ st[r -- _length] .intval ≤ sk .index) ∧ fits(st[r -- sk] .refval, sks0, st)

Rule argument

[x0lemmaarg: spec-name: list-data instance-name: storekeys lemma-name: elim-list-c antecedent: sks ≠ [] succedent: sk = sks .first ∧ sks0 = sks .rest ↔ sks = sk + sks0 substlist: [sks, sk, sks0] → [sks, sk, sks0] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : sks ≠ [] ⊦ sk = sks .first ∧ sks0 = sks .rest ↔ sks = sk + sks0])], [EXTRATERMS : (sks, sk, sks0)]]