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Proof step 82 from proof hasSharing-put-index-refval (previous step)

st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r1)][r0 -- (sks + i ' ' + sks1)]) = refval(r1), st[r0 -- sks] = refval(r0), (st[r0 -- i ', refval(r1)][r0 -- sks]) = refval(r), disjoint(str, r0 ' + r1 ', st), validref(str, r1, ty, st), fits(r0, sks, st[r0 -- i ', refval(r1)]), fits(r, i ' ' + sks1, st[r0 -- i ', refval(r1)]), i < st[r0 -- _length] .intval, 0 ≤ i, 0 < st[r0 -- _length] .intval ⊦ sks + i ' ' + sks1 = i ' ', r0 = jvmref, r0 = r1, r1 = jvmref, junkref(str, r0, st), hasSharing(r1, st), hasSharing(r0, st), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r0 -- sks2] .refval ≠ r0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ sks ≠ [] → ( fits(r, sks, st) ↔ r ≠ jvmref ∧ is_referencevalue(st[r -- sks .first]) ∧ (is_classtype(st[r -- _type] .type) → sks .first ∈ instfields(st[r -- _type] .type .class)) ∧ (is_arraytype(st[r -- _type] .type) → is_indexkey(sks .first) ∧ 0 ≤ sks .first .index ∧ sks .first .index < st[r -- _length] .intval) ∧ fits(st[r -- sks .first] .refval, sks .rest, st))
Proof step 81:
i ' ' + sks1 ≠ [], st[r0 -- _type] .type = mkarraytype(ty), (st[r0 -- i ', refval(r1)][r0 -- (sks + i ' ' + sks1)]) = refval(r1), st[r0 -- sks] = refval(r0), (st[r0 -- i ', refval(r1)][r0 -- sks]) = refval(r), disjoint(str, r0 ' + r1 ', st), validref(str, r1, ty, st), fits(r0, sks, st[r0 -- i ', refval(r1)]), r ≠ jvmref ∧ is_referencevalue(st[r0 -- i ', refval(r1)][r -- (i ' ' + sks1) .first]) ∧ ( is_classtype((st[r0 -- i ', refval(r1)][r -- _type]) .type) → (i ' ' + sks1) .first ∈ instfields((st[r0 -- i ', refval(r1)][r -- _type]) .type .class)) ∧ ( is_arraytype((st[r0 -- i ', refval(r1)][r -- _type]) .type) → is_indexkey((i ' ' + sks1) .first) ∧ 0 ≤ (i ' ' + sks1) .first .index ∧ (i ' ' + sks1) .first .index < (st[r0 -- i ', refval(r1)][r -- _length]) .intval) ∧ fits((st[r0 -- i ', refval(r1)][r -- (i ' ' + sks1) .first]) .refval, (i ' ' + sks1) .rest, st[r0 -- i ', refval(r1)]), i < st[r0 -- _length] .intval, 0 ≤ i, 0 < st[r0 -- _length] .intval ⊦ sks + i ' ' + sks1 = i ' ', r0 = jvmref, r0 = r1, r1 = jvmref, junkref(str, r0, st), hasSharing(r1, st), hasSharing(r0, st), ∃ sks2. ¬ (sks2 + i ' ' ⊑ sks → st[r0 -- sks2] .refval ≠ r0)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: fits-rec antecedent: succedent: sks ≠ [] → ( fits(r, sks, st) ↔ r ≠ jvmref ∧ is_referencevalue(st[r -- sks .first]) ∧ ( is_classtype(st[r -- _type] .type) → sks .first ∈ instfields(st[r -- _type] .type .class)) ∧ ( is_arraytype(st[r -- _type] .type) → is_indexkey(sks .first) ∧ 0 ≤ sks .first .index ∧ sks .first .index < st[r -- _length] .intval) ∧ fits(st[r -- sks .first] .refval, sks .rest, st)) substlist: [st, sks, r] → [st[r0 -- i ', refval(r1)], i ' ' + sks1, r] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 7)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, storekeys, app-02-ant, ⊦ ¬ sks + sks0 ≠ [] ↔ sks = [] ∧ sks0 = []], [CSIMPNAMEDSEQ : list, storekeys, e, ⊦ sk ' ≠ []], [CSIMPNAMEDSEQ : list, storekeys, a, ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1])], [EXTRATERMS : (st[r0 -- i ', refval(r1)], i ' ' + sks1, r)]]