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Proof step 76 from proof addarray-disjoint-nosharing (previous step)

(addarray(r, ty, mkjavavalues(refs), st)[refs[i→n(i)] -- sks1]) = refval(r0), (addarray(r, ty, mkjavavalues(refs), st)[refs[i→n(i0)] -- sks]) = refval(r0), i < n→i(# refs), i0 < n→i(# refs), i→n(i0) < # refs, 0 ≤ i, newref(r, st), validreflist(str, mkjavavalues(refs), ty, st), disjoint(str, refs, st), fits(refs[i→n(i)], sks1, addarray(r, ty, mkjavavalues(refs), st)), fits(refs[i→n(i0)], sks, st), 0 ≤ i0, i→n(i) < # refs, is_referencevalue(addarray(r, ty, mkjavavalues(refs), st)[r -- (i0 ' ' + sks)]), is_referencevalue(addarray(r, ty, mkjavavalues(refs), st)[r -- (i ' ' + sks1)]), st ⊆ addarray(r, ty, mkjavavalues(refs), st) ⊦ r0 = jvmref, refs = [], r = jvmref, i0 ' ' + sks = i ' ' + sks1, junkref(str, refs[i→n(i0)], st), hasSharing(refs, st), dups(refs)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ st ⊆ st0 ∧ ¬ junkref(str, r, st) → (fits(r, sks, st0) ↔ fits(r, sks, st))
Proof step 33:
¬ (st ⊆ addarray(r, ty, mkjavavalues(refs), st) ∧ ¬ junkref(str, refs[i→n(i)], st)), (addarray(r, ty, mkjavavalues(refs), st)[refs[i→n(i)] -- sks1]) = refval(r0), (addarray(r, ty, mkjavavalues(refs), st)[refs[i→n(i0)] -- sks]) = refval(r0), i < n→i(# refs), i0 < n→i(# refs), i→n(i0) < # refs, 0 ≤ i, newref(r, st), validreflist(str, mkjavavalues(refs), ty, st), disjoint(str, refs, st), fits(refs[i→n(i)], sks1, addarray(r, ty, mkjavavalues(refs), st)), fits(refs[i→n(i0)], sks, st), 0 ≤ i0, i→n(i) < # refs, is_referencevalue(addarray(r, ty, mkjavavalues(refs), st)[r -- (i0 ' ' + sks)]), is_referencevalue(addarray(r, ty, mkjavavalues(refs), st)[r -- (i ' ' + sks1)]), st ⊆ addarray(r, ty, mkjavavalues(refs), st) ⊦ r0 = jvmref, refs = [], r = jvmref, i0 ' ' + sks = i ' ' + sks1, junkref(str, refs[i→n(i0)], st), hasSharing(refs, st), dups(refs)
Proof step 75:
st ⊆ addarray(r, ty, mkjavavalues(refs), st) ∧ ¬ junkref(str, refs[i→n(i)], st), (addarray(r, ty, mkjavavalues(refs), st)[refs[i→n(i)] -- sks1]) = refval(r0), (addarray(r, ty, mkjavavalues(refs), st)[refs[i→n(i0)] -- sks]) = refval(r0), i < n→i(# refs), i0 < n→i(# refs), i→n(i0) < # refs, 0 ≤ i, newref(r, st), validreflist(str, mkjavavalues(refs), ty, st), disjoint(str, refs, st), fits(refs[i→n(i)], sks1, st), fits(refs[i→n(i0)], sks, st), 0 ≤ i0, i→n(i) < # refs, is_referencevalue(addarray(r, ty, mkjavavalues(refs), st)[r -- (i0 ' ' + sks)]), is_referencevalue(addarray(r, ty, mkjavavalues(refs), st)[r -- (i ' ' + sks1)]), st ⊆ addarray(r, ty, mkjavavalues(refs), st) ⊦ r0 = jvmref, refs = [], r = jvmref, i0 ' ' + sks = i ' ' + sks1, junkref(str, refs[i→n(i0)], st), hasSharing(refs, st), dups(refs)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: fits-subset-01 antecedent: succedent: st ⊆ st0 ∧ ¬ junkref(str, r, st) → (fits(r, sks, st0) ↔ fits(r, sks, st)) substlist: [st, st0, str, r, sks] → [st, addarray(r, ty, mkjavavalues(refs), st), str, refs[i→n(i)], sks1] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 9)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, addarray(r, ty, mkjavavalues(refs), st), str, refs[i→n(i)], sks1)]]