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Proof step 46 from proof pathex-put-nopathex (previous step)

refs0 = r1 + refs1, r1 = (st[r0 -- sk, val][r -- fs ']) .refval, is_obj(str, r, st[r0 -- sk, val]), fs ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r0 -- sk, val][r -- fs ']), validrefs(str, refs0, fs .type, st[r0 -- sk, val]), ∀ val, sk, r0, st, r, str, refs. # refs < # refs0 → ( validrefs(str, r ' + refs, st[r -- _type] .type, st[r0 -- sk, val]) → sk = _type ∨ path∃(str, r, r0, st) ∨ junkref(str, r, st) ∨ path∃(str, r, (r ' + refs) .last, st)) ⊦ sk = _type, r = jvmref, refs0 = [], junkref(str, r, st), path∃(str, r, r0, st), path∃(str, r, refs0 .last, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
is_obj(str, r, st[r0 -- sk, val]), fs ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r0 -- sk, val][r -- fs ']), validrefs(str, (st[r0 -- sk, val][r -- fs ']) .refval ' + refs1, fs .type, st[r0 -- sk, val]), ∀ val0, sk0, r3, st0, r2, str, refs. # refs < # ((st[r0 -- sk, val][r -- fs ']) .refval + refs1) → ( validrefs(str, r2 ' + refs, st0[r2 -- _type] .type, st0[r3 -- sk0, val0]) → sk0 = _type ∨ path∃(str, r2, r3, st0) ∨ junkref(str, r2, st0) ∨ path∃(str, r2, (r2 ' + refs) .last, st0)) ⊦ sk = _type, r = jvmref, junkref(str, r, st), path∃(str, r, r0, st), path∃(str, r, ((st[r0 -- sk, val][r -- fs ']) .refval ' + refs1) .last, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]