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Proof step 51 from proof validrefs-put-notin-02 (previous step)

validrefs(str, (r1 ' + acc) + r0 ', ty, st), okval(val, ty0), is_valid_ref(str, r1, st), st[r1 -- _type] .type ≤ ty, ∀ str, r0, ty, st, val, ty0, class, fieldvar, r. validrefs(str, acc + r0 ', ty, st) ∧ okval(val, ty0) → mkfs(class, ty0, fieldvar) ' = _length ∨ mkfs(class, ty0, fieldvar) ' = _type ∨ validrefs(str, acc + r0 ', ty, st[r -- mkfs(class, ty0, fieldvar) ', val]) ∨ r ∈ acc ⊦ r1 = jvmref, r = r1, mkfs(class, ty0, fieldvar) ' = _type, mkfs(class, ty0, fieldvar) ' = _length, r ∈ acc, validrefs(str, (r1 ' + acc) + r0 ', ty, st[r -- mkfs(class, ty0, fieldvar) ', val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ is_valid_ref(str, r, st) ↔ is_obj(str, r, st) ∨ is_array(str, r, st)
Proof step 50:
validrefs(str, (r1 ' + acc) + r0 ', ty, st), okval(val, ty0), is_obj(str, r1, st) ∨ is_array(str, r1, st), st[r1 -- _type] .type ≤ ty, ∀ str, r0, ty, st, val, ty0, class, fieldvar, r. validrefs(str, acc + r0 ', ty, st) ∧ okval(val, ty0) → mkfs(class, ty0, fieldvar) ' = _length ∨ mkfs(class, ty0, fieldvar) ' = _type ∨ validrefs(str, acc + r0 ', ty, st[r -- mkfs(class, ty0, fieldvar) ', val]) ∨ r ∈ acc ⊦ r1 = jvmref, r = r1, mkfs(class, ty0, fieldvar) ' = _type, mkfs(class, ty0, fieldvar) ' = _length, r ∈ acc, validrefs(str, (r1 ' + acc) + r0 ', ty, st[r -- mkfs(class, ty0, fieldvar) ', val])

Rule argument

[speclemmaarg: ,is_valid_ref(str, r, st) ↔ is_obj(str, r, st) ∨ is_array(str, r, st) ,[st, r, str] → [st, r1, str] ,F ,addfuns , ,is-valid-ref-stronger-def ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r1, str)]]