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Proof step 119 from proof pathex-put-nopathex (previous step)

st[r -- mkfs(class, ty, fieldvar) '] = refval(r1), is_obj(str, r, st), validrefs(str, r1 ' + refs1, ty, st), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), path∃(str, r1, r0, st) ∨ junkref(str, r1, st) ∨ path∃(str, r1, (r1 ' + refs1) .last, st[r0 -- sk, val]), ∀ val, r0, sk, st0, r2, str, refs. # refs < # (r1 + refs1) → ( validrefs(str, r2 ' + refs, st0[r2 -- _type] .type, st0) → sk = _type ∨ path∃(str, r2, r0, st0) ∨ junkref(str, r2, st0) ∨ path∃(str, r2, (r2 ' + refs) .last, st0[r0 -- sk, val])) ⊦ r1 = jvmref, r = (r1 ' + refs1) .last, r = r0, r = jvmref, sk = _type, st[r1 -- _type] .type ≤ ty ∧ path∃(str, r1, r0, st), (is_reftype(ty) ∨ ty = abstract_type) ∧ (¬ st[r1 -- _type] .type ≤ ty ∨ junkref(str, r1, st)), st[r1 -- _type] .type ≤ ty ∧ path∃(str, r1, (r1 ' + refs1) .last, st[r0 -- sk, val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 118:
⊦ r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → ¬ validrefs(str, r ' + refs, ty, st)

Rule argument

[crewrite-arg: validrefs-is-junk , F , [st, ty, refs, r, str] → [st, ty, refs1, r1, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_reftype(ty0) → (ty ≤ ty0 ↔ ty = ty0)], [CSIMPSEQ : ⊦ ¬ is_reftype (st[r -- _type] .type) → ¬ is_valid_ref(str, r, st)])], [EXTRATERMS : (st, ty, refs1, r1, str)]]