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Proof step 9 from proof is_valid_ref-put-equiv (previous step)

okval(st[r1 -- mkfs(class, ty, fieldvar) '], ty), r1 -- mkfs(class, ty, fieldvar) ' ∈ st, okval(val, ty), r1 ∈ st ⊦ mkfs(class, ty, fieldvar) ' = _length, ty = void_type, class+∃(str, st[r -- _type] .type .class) ∧ ¬ is_abstract(st[r -- _type] .type .class) ∧ is_obj(r, st) ∨ is_array(str, r, st[r1 -- mkfs(class, ty, fieldvar) ', val]) ↔ is_obj(str, r, st) ∨ is_array(str, r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ fs ' ≠ _length ∧ fs ' ≠ _type → (is_array(str, r, st[r0 -- fs ', val]) ↔ is_array(str, r, st))
Proof step 8:
⊦ is_obj(str, r, st) ↔ class+∃(str, st[r -- _type] .type .class) ∧ ¬ is_abstract(st[r -- _type] .type .class) ∧ is_obj(r, st)

Rule argument

[speclemmaarg: , fs ' ≠ _length ∧ fs ' ≠ _type → (is_array(str, r, st[r0 -- fs ', val]) ↔ is_array(str, r, st)) ,[val, fs, r0, st, r, str] → [val, mkfs(class, ty, fieldvar), r1, st, r, str] ,F ,okfuns , ,is_array-put-field ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty ≠ void_type → mkfs(class, ty, fieldvar) ' ≠ _type])], [EXTRATERMS : (val, mkfs(class, ty, fieldvar), r1, st, r, str)]]