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Proof step 47 from proof validval-put-any (previous step)

sk .fs = mkfs(class0, ty0, fieldvar0), validref(str, r0, ty, st), is_reftype(ty), is_indexkey(sk), okval(refval(r2), st[r1 -- _type] .type .type), validref(str, r2, st[r1 -- _type] .type .type, st), r ≠ r1 ∨ _type ≠ sk ⊦ ty = void_type, mkfs(class, ty, fieldvar) ' = _length, validref(str, r0, ty, st[r1 -- sk, refval(r2)]), r1 ≠ jvmref ∧ is_arraytype(st[r1 -- _type] .type) ∧ (r2 = jvmref → is_reftype(st[r1 -- _type] .type .type))

User applied rule case distinction

And obtained the following new goals

Proof step 28:
⊦ validref(str, r, ty1, st[jvmref -- sk, val]) ↔ validref(str, r, ty1, st)
Proof step 33:
sk .fs = mkfs(class0, ty0, fieldvar0), validref(str, r0, ty, st), is_reftype(ty), is_indexkey(sk), okval(refval(r2), st[r1 -- _type] .type .type), validref(str, r2, st[r1 -- _type] .type .type, st), r ≠ r1 ∨ _type ≠ sk ⊦ is_arraytype(st[r1 -- _type] .type), ty = void_type, mkfs(class, ty, fieldvar) ' = _length, validref(str, r0, ty, st[r1 -- sk, refval(r2)])
Proof step 46:
sk .fs = mkfs(class0, ty0, fieldvar0), validref(str, r0, ty, st), is_reftype(ty), is_indexkey(sk), okval(refval(r2), st[r1 -- _type] .type .type), validref(str, r2, st[r1 -- _type] .type .type, st), r ≠ r1 ∨ _type ≠ sk ⊦ r2 = jvmref → is_reftype(st[r1 -- _type] .type .type), ty = void_type, mkfs(class, ty, fieldvar) ' = _length, validref(str, r0, ty, st[r1 -- sk, refval(r2)])

Rule argument

[CASEDARG : pos: right 4, ()]

Additional information

[[CONCRETESIMPRULES : ()]]