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Proof step 115 from proof validval-put-any (previous step)

sk .fs = mkfs(class, ty, fieldvar), sk0 .fs = mkfs(class0, ty0, fieldvar0), validref(str, r0, st[r -- _type] .type .type, st), okval(refval(r0), st[r -- _type] .type .type), is_indexkey(sk), is_indexkey(sk0), okval(refval(r2), st[r1 -- _type] .type .type), validref(str, r2, st[r1 -- _type] .type .type, st), r ≠ r1 ∨ _type ≠ sk0 ⊦ validref(str, r0, st[r -- _type] .type .type, st[r1 -- sk0, 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 96:
⊦ validref(str, r, ty1, st[jvmref -- sk, val]) ↔ validref(str, r, ty1, st)
Proof step 101:
sk .fs = mkfs(class, ty, fieldvar), sk0 .fs = mkfs(class0, ty0, fieldvar0), validref(str, r0, st[r -- _type] .type .type, st), okval(refval(r0), st[r -- _type] .type .type), is_indexkey(sk), is_indexkey(sk0), okval(refval(r2), st[r1 -- _type] .type .type), validref(str, r2, st[r1 -- _type] .type .type, st), r ≠ r1 ∨ _type ≠ sk0 ⊦ is_arraytype(st[r1 -- _type] .type), validref(str, r0, st[r -- _type] .type .type, st[r1 -- sk0, refval(r2)])
Proof step 114:
sk .fs = mkfs(class, ty, fieldvar), sk0 .fs = mkfs(class0, ty0, fieldvar0), validref(str, r0, st[r -- _type] .type .type, st), okval(refval(r0), st[r -- _type] .type .type), is_indexkey(sk), is_indexkey(sk0), okval(refval(r2), st[r1 -- _type] .type .type), validref(str, r2, st[r1 -- _type] .type .type, st), r ≠ r1 ∨ _type ≠ sk0 ⊦ r2 = jvmref → is_reftype(st[r1 -- _type] .type .type), validref(str, r0, st[r -- _type] .type .type, st[r1 -- sk0, refval(r2)])

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]