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Proof step 41 from proof pathex-put-nopathex (previous step)

(st[r0 -- sk, val][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[r0 -- sk, val]), ∀ 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)) ⊦ r = jvmref, sk = _type, 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 7:
⊦ rk ≠ rk0 → (st[rk0, val][rk]) = st[rk]
Proof step 8:
⊦ path∃(str, r, r, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st)
Proof step 40:
r -- mkfs(class, ty, fieldvar) ' ≠ r0 -- sk, 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[r0 -- sk, val]), ∀ 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)) ⊦ r = jvmref, sk = _type, path∃(str, r, (r1 ' + refs1) .last, st), path∃(str, r, r0, st), junkref(str, r, st)

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk]) = st[rk] ,[rk, val, rk0, st] → [r -- mkfs(class, ty, fieldvar) ', val, r0 -- sk, st] ,F ,store ,javastore-ostorea ,At-other ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ (st[rk, val][rk]) = val], [CSIMPSEQ : ⊦ ¬ is_valid_ref(str, r, st) ∧ r ≠ jvmref → junkref(str, r, st)])], [EXTRATERMS : (r -- mkfs(class, ty, fieldvar) ', val, r0 -- sk, st)]]