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Proof step 18 from proof unchanged-lookup-list-generic (previous step)

is_obj(str, r, st), st0[r -- sk] = st[r -- sk], is_obj(str, r, st), junkref(str, st[r -- sk] .refval, st), unchanged(str, st[r -- sk] .refval, st, st0), unchanged(str, r, st, st0), fits(st[r -- sk] .refval, sks0, st0), fits(st[r -- sk] .refval, sks0, st), is_referencevalue(st[r -- sk]), is_classtype(st[r -- _type] .type), sk ∈ instfields(st[r -- _type] .type .class), is_classtype(st0[r -- _type] .type) → sk ∈ instfields(st0[r -- _type] .type .class), is_arraytype(st0[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st0[r -- _length] .intval ⊦ sks0 = [], st[st[r -- sk] .refval -- sks0] = st0[st[r -- sk] .refval -- sks0], r = jvmref, sk .fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- sk .fs ']) ∧ st[r -- sk .fs '] .refval ≠ jvmref ∧ (¬ st[st[r -- sk .fs '] .refval -- _type] .type ≤ sk .fs .type ∨ junkref(str, st[r -- sk .fs '] .refval, st)), junkref(str, r, st0)

User applied rule insert elim lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: storekey instance-name: lemma-name: elim-03 antecedent: succedent: is_fskey(sk) → (fs = sk .fs ↔ sk = fs ') substlist: [sk, fs] → [sk, fs] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : addfuns, , instfields-index-01, ⊦ is_indexkey(sk) → ¬ sk ∈ instfields(class)], [CSIMPNAMEDSEQ : storekey, , test-01, ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)], [CSIMPNAMEDSEQ : storekey, , test-05, ⊦ is_fskey(fs ')], [CSIMPNAMEDSEQ : storekey, , test-07, ⊦ ¬ is_indexkey(fs ')], [CSIMPNAMEDSEQ : junkrefs, , junkref-bad-type, ⊦ ¬ is_classtype (st[r -- _type] .type) ∧ ¬ is_arraytype (st[r -- _type] .type) → ( junkref(str, r, st) ↔ r ≠ jvmref)], [CSIMPNAMEDSEQ : javatype, , diff, ⊦ is_classtype(ty) → ¬ is_arraytype(ty)], [CSIMPELIM : ⊦ is_fskey(sk) → (fs = sk .fs ↔ sk = fs ')])], [EXTRATERMS : (sk, fs)]]