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Proof step 80 from proof pathex-put-nopathex (previous step)

(st[r0 -- sk, val][r -- i ']) = refval(r1), validrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st[r0 -- sk, val]), i < (st[r0 -- sk, val][r -- _length]) .intval, is_array(str, r, st[r0 -- sk, val]), 0 < (st[r0 -- sk, val][r -- _length]) .intval, 0 ≤ i, ∀ 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 52:
⊦ rk ≠ rk0 → (st[rk0, val][rk]) = st[rk]
Proof step 53:
⊦ path∃(str, r, r, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st)
Proof step 79:
r -- _length ≠ r0 -- sk, (st[r0 -- sk, val][r -- i ']) = refval(r1), validrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st[r0 -- sk, val]), i < st[r -- _length] .intval, is_array(str, r, st[r0 -- sk, val]), 0 < st[r -- _length] .intval, 0 ≤ i, ∀ 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 -- _length, val, r0 -- sk, st] ,F ,store ,javastore-ostorea ,At-other ]

Additional information

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