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Proof step 40 from proof validrefs-put-array-badindex (previous step)

(st[r -- i ', val][r0 -- i0 ']) = refval(r2), i < st[r0 -- _length] .intval, i0 < st[r0 -- _length] .intval, validrefs(str, r2 ' + refs, st[r0 -- _type] .type .type, st[r -- i ', val]), is_array(str, r0, st), i < 0, is_array(str, r0, st[r -- i ', val]), st[r0 -- _type] .type ≤ ty, 0 ≤ i0, 0 < st[r0 -- _length] .intval, ∀ i1, str0, ty0, st0, r1, val0. ¬ 0 ≤ i1 → (validrefs(str0, r2 ' + refs, ty0, st0[r1 -- i1 ', val0]) ↔ validrefs(str0, r2 ' + refs, ty0, st0)) ⊦ r0 = jvmref, ∃ i1. ¬ i1 < 0 ∧ ¬ st[r0 -- _length] .intval ≤ i1 ∧ is_referencevalue(st[r0 -- i1 ']) ∧ r2 = st[r0 -- i1 '] .refval ∧ validrefs(str, st[r0 -- i1 '] .refval ' + refs, st[r0 -- _type] .type .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[x0lemmaarg: spec-name: store instance-name: javastore lemma-name: At-other antecedent: succedent: rk ≠ rk0 → (st[rk0, val][rk]) = st[rk] substlist: [rk, val, rk0, st] → [r0 -- i0 ', val, r -- i ', st] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 0, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : refkey, , inj, ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPNAMEDSEQ : storekey, , inj-04, ⊦ i ' = i0 ' ↔ i = i0], [CSIMPNAMEDFORWARD : oelem, intlista, lel, ⊦ i < i0 ∧ i = i1 → i1 < i0], [CSIMPNAMEDSEQ : store, javastore, At-same, ⊦ (st[rk, val][rk]) = val], [CSIMPNAMEDSEQ : int-abs, , lels-04, ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])], [EXTRATERMS : (r0 -- i0 ', val, r -- i ', st)]]