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Proof step 104 from proof pathex-put-pathex-array-refval (previous step)

st[r0 -- _type] .type = mkarraytype(ty), 0 ≤ i, 0 < st[r0 -- _length] .intval, validref(str, r2, ty, st), i < st[r0 -- _length] .intval, path∃(str, r, r0, st), validrefs(str, r ' + refs0, st[r -- _type] .type, st[r0 -- i ', refval(r2)]), r0 ∈ refs0, r2 = jvmref → is_reftype(ty) ⊦ r = r0, r0 = jvmref, r = refs0 .last, dups(refs0), r ∈ refs0, path∃(str, r2, refs0 .last, st), path∃(str, r, refs0 .last, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ r ∈ refs ↔ (∃ refs0, refs1. refs = refs0 + (r + refs1))
Proof step 103:
st[r0 -- _type] .type = mkarraytype(ty), 0 ≤ i, 0 < st[r0 -- _length] .intval, validref(str, r2, ty, st), i < st[r0 -- _length] .intval, path∃(str, r, r0, st), validrefs(str, r ' + refs0, st[r -- _type] .type, st[r0 -- i ', refval(r2)]), ∃ refs2, refs1. refs0 = refs2 + (r0 + refs1), r2 = jvmref → is_reftype(ty) ⊦ r = r0, r0 = jvmref, r = refs0 .last, dups(refs0), r ∈ refs0, path∃(str, r2, refs0 .last, st), path∃(str, r, refs0 .last, st)

Rule argument

[x0lemmaarg: spec-name: list instance-name: references lemma-name: In antecedent: succedent: r ∈ refs ↔ (∃ refs0, refs1. refs = refs0 + (r + refs1)) substlist: [refs, r] → [refs0, r0] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 7)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (refs0, r0)]]