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Proof step 12 from proof pathex-put-nopathex (previous step)

st[r -- mkfs(class, ty, fieldvar) '] = refval(r1), validrefs(str, r1 ' + refs1, ty, st[r0 -- sk, val]), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), ∀ val0, sk0, r3, st0, r2, str, refs. # refs < # (r1 + 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)) ⊦ validrefs(str, r1 ' + refs1, st[r1 -- _type] .type, st[r0 -- sk, val]), r = jvmref, sk = _type, r = r0, path∃(str, r, (r1 ' + refs1) .last, st), path∃(str, r, r0, st), junkref(str, r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ validrefs(str, refs, ty, st) ∧ ty0 = st[r -- _type] .type ∧ refs ≠ [] ∧ refs .first ≠ jvmref ∧ r = refs .first → validrefs(str, refs, ty0, st)
Proof step 11:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []

Rule argument

[crewrite-arg: validrefs-sametype-03 , F , [str, refs, ty, st, ty0, r] → [str, r1 ' + refs1, ty, st[r0 -- sk, val], st[r1 -- _type] .type, (r1 ' + refs1) .first] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []])], [EXTRATERMS : (str, r1 ' + refs1, ty, st[r0 -- sk, val], st[r1 -- _type] .type, (r1 ' + refs1) .first)]]