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Proof step 29 from proof is_valid_ref-put (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ is_array(str, r, st) ↔ type∃(str, st[r -- _type] .type) ∧ st[r -- _type] .type .jtelemtype ≠ void_type ∧ st[r -- _type] .type .jtelemtype ≠ abstract_type ∧ is_array(r, st)
Proof step 28:
okval(val, ty), is_valid_ref(r, st) ⊦ mkfs(class, ty, fieldvar) ' = _length, ty = void_type, is_obj(str, r, st[r1 -- mkfs(class, ty, fieldvar) ', val]), type∃(str, (st[r1 -- mkfs(class, ty, fieldvar) ', val][r -- _type]) .type) ∧ (st[r1 -- mkfs(class, ty, fieldvar) ', val][r -- _type]) .type .jtelemtype ≠ void_type ∧ (st[r1 -- mkfs(class, ty, fieldvar) ', val][r -- _type]) .type .jtelemtype ≠ abstract_type ∧ is_array(r, st[r1 -- mkfs(class, ty, fieldvar) ', val]), (¬ class+∃(str, st[r -- _type] .type .class) ∨ is_abstract(st[r -- _type] .type .class) ∨ ¬ is_obj(r, st)) ∧ ¬ is_array(str, r, st)

Rule argument

[speclemmaarg: , is_array(str, r, st) ↔ type∃(str, st[r -- _type] .type) ∧ st[r -- _type] .type .jtelemtype ≠ void_type ∧ st[r -- _type] .type .jtelemtype ≠ abstract_type ∧ is_array(r, st) ,[st, r, str] → [st[r1 -- mkfs(class, ty, fieldvar) ', val], r, str] ,F ,okfuns , ,is-real-array-def ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r1 -- mkfs(class, ty, fieldvar) ', val], r, str)]]