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Proof step 164 from proof pathex-put-nopathex (previous step)

st[r -- i '] = refval(r1), validrefs(str, r1 ' + refs1, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, st[r1 -- _type] .type ≤ st[r -- _type] .type .type, path∃(str, r1, r0, st) ∨ path∃(str, 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])) ⊦ refs1 = [], r = jvmref, sk = _type, r1 = jvmref, path∃(str, r, r0, st), path∃(str, r, refs1 .last, st[r0 -- sk, val]), junkref(str, r1, st), is_array(str, r, st[r0 -- sk, val]) ∧ r ≠ refs1 .last

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 161:
⊦ r ≠ r0 → (is_array(str, r0, st[r -- sk, val]) ↔ is_array(str, r0, st))
Proof step 162:
⊦ path∃(str, r, r, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st)
Proof step 163:
⊦ path∃(str, r, r, st) ↔ r = jvmref ∨ r ≠ jvmref ∧ is_valid_ref(str, r, st)

Rule argument

[speclemmaarg: , r ≠ r0 → (is_array(str, r0, st[r -- sk, val]) ↔ is_array(str, r0, st)) ,[val, sk, r, st, r0, str] → [val, sk, r0, st, r, str] ,F ,okfuns , ,is_array-put-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → ( is_valid_ref (str, r0, st[r -- sk, val]) ↔ is_valid_ref(str, r0, st))], [CSIMPSEQ : ⊦ is_array(str, r, st) → is_valid_ref(str, r, st)])], [EXTRATERMS : (val, sk, r0, st, r, str)]]