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Proof step 39 from proof unchanged-lookup-list-generic (previous step)

is_obj(str, r, st0), is_obj(str, r, st0), junkref(str, st0[r -- sk] .refval, st0), unchanged(str, st0[r -- sk] .refval, st, st0), unchanged(str, r, st, st0), fits(st0[r -- sk] .refval, sks0, st0), fits(st0[r -- sk] .refval, sks0, st), is_referencevalue(st0[r -- sk]), is_valid_ref(str, r, st), is_classtype(st0[r -- _type] .type), sk ∈ instfields(st0[r -- _type] .type .class), is_arraytype(st[r -- _type] .type) → is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval, is_classtype(st[r -- _type] .type) → sk ∈ instfields(st[r -- _type] .type .class), is_arraytype(st[r -- _type] .type) → sk = _length ∨ is_indexkey(sk) ∧ 0 ≤ sk .index ∧ sk .index < st[r -- _length] .intval ⊦ sks0 = [], st[st0[r -- sk] .refval -- sks0] = st0[st0[r -- sk] .refval -- sks0], r = jvmref, junkref(str, r, st), sk .fs ' ∈ instfields(st0[r -- _type] .type .class) ∧ is_referencevalue(st0[r -- sk .fs ']) ∧ st0[r -- sk .fs '] .refval ≠ jvmref ∧ (¬ st0[st0[r -- sk .fs '] .refval -- _type] .type ≤ sk .fs .type ∨ junkref(str, st0[r -- sk .fs '] .refval, st0)), ∃ fs. fs ' ∈ instfields(st0[r -- _type] .type .class) ∧ is_referencevalue(st0[r -- fs ']) ∧ st0[r -- fs '] .refval ≠ jvmref ∧ (¬ st0[st0[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ junkref(str, st0[r -- fs '] .refval, 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, fs0] 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 : addfuns, , is_valid_ref-no-arraytype, ⊦ ¬ is_arraytype (st[r -- _type] .type) → ( is_valid_ref(str, r, st) ↔ is_obj(str, r, st))], [CSIMPNAMEDSEQ : addfuns, , is_obj-classtype, ⊦ ¬ is_classtype (st[r -- _type] .type) → ¬ is_obj(str, r, st)], [CSIMPNAMEDSEQ : javatype, , diff, ⊦ is_classtype(ty) → ¬ is_arraytype(ty)], [CSIMPELIM : ⊦ is_fskey(sk) → (fs = sk .fs ↔ sk = fs ')])], [EXTRATERMS : (sk, fs0)]]