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Proof step 25 from proof validrefs-junkrefs-append (previous step)

st[r -- i '] = refval(r0), validrefs(str, r0 ' + refs2, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, junkrefs(str, (r0 ' + refs2) .last ' + refs1, st[(r0 ' + refs2) .last -- _type] .type, st), is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, ∀ str0, ty0, st0, refs. validrefs(str0, r0 ' + refs2, ty0, st0) ∧ junkrefs(str0, (r0 ' + refs2) .last ' + refs, st0[(r0 ' + refs2) .last -- _type] .type, st0) → junkrefs(str0, (r0 ' + refs2) + refs, ty0, st0) ⊦ r = jvmref, junkrefs(str, r ' + (r0 ' + refs2) + refs1, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( junkrefs(str, r ' + refs, ty, st) ↔ refs ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs .first = st[r -- i '] .refval ∧ junkrefs(str, refs, st[r -- _type] .type .type, st)))
Proof step 24:
is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty, st[r -- i '] = refval(r0), validrefs(str, r0 ' + refs2, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, junkrefs(str, (r0 ' + refs2) .last ' + refs1, st[(r0 ' + refs2) .last -- _type] .type, st), is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, ∀ str0, ty0, st0, refs. validrefs(str0, r0 ' + refs2, ty0, st0) ∧ junkrefs(str0, (r0 ' + refs2) .last ' + refs, st0[(r0 ' + refs2) .last -- _type] .type, st0) → junkrefs(str0, (r0 ' + refs2) + refs, ty0, st0) ⊦ r = jvmref, (r0 ' + refs2) + refs1 ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ ((r0 ' + refs2) + refs1) .first = st[r -- i '] .refval ∧ junkrefs(str, (r0 ' + refs2) + refs1, st[r -- _type] .type .type, st))

Rule argument

[x0lemmaarg: spec-name: junkrefs instance-name: lemma-name: junkrefs-array antecedent: succedent: is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( junkrefs(str, r ' + refs, ty, st) ↔ refs ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs .first = st[r -- i '] .refval ∧ junkrefs (str, refs, st[r -- _type] .type .type, st))) substlist: [st, ty, refs, r, str] → [st, ty, (r0 ' + refs2) + refs1, r, str] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, (r0 ' + refs2) + refs1, r, str)]]