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Proof step 79 from proof unchanged-junkrefs-level (previous step)

st1[r -- _type] = st[r -- _type], st1[r -- i '] = refval(r1), st[r -- _length] = st1[r -- _length], st[r -- _type] .type = mkarraytype(ty1), st[r -- i '] = refval(r1), st1[r1 -- _type] .type ≤ ty1, is_valid_ref(str, r1, st1), level⊆(str, str0), unchanged(str0, r, st, st1), junkrefs(str, r1 ' + refs, ty1, st), i < st1[r -- _length] .intval, mkarraytype(ty1) ≤ ty, is_array(str, r, st1), 0 ≤ i, is_array(str, r, st), unchangedNorec(r, st, st1), is_array(str0, r, st), 0 < st1[r -- _length] .intval, is_array(str0, r, st1), ∀ r0. (path∃(str0, r, r0, st) ↔ path∃(str0, r, r0, st1)) ∧ (path∃(str0, r, r0, st) → unchangedNorec(r0, st, st1)), ∀ i0. ¬ i0 < 0 ∧ ¬ st1[r -- _length] .intval ≤ i0 → st[r -- i0 '] = st1[r -- i0 '] ⊦ r = r1, r = jvmref, r1 = jvmref, unchanged(str0, r1, st, st1), junkrefs(str, r1 ' + refs, ty1, st1), is_valid_ref(str0, r1, st1), st[r1 -- _type] .type ≤ ty1 ∧ is_valid_ref(str0, r1, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: junkrefs instance-name: lemma-name: is_valid_ref-levelsubset antecedent: succedent: level⊆(str, str0) ∧ is_valid_ref(str, r, st) → is_valid_ref(str0, r, st) substlist: [str, str0, r, st] → [str, str0, r1, st1] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 5)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (str, str0, r1, st1)]]