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Proof step 46 from proof validrefs-put-notin-03 (previous step)

st[r -- i '] = refval(r0), i < st[r -- _length] .intval, validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st[r -- sk, val]), is_array(str, r, st), is_valid_ref(r, st), is_array(str, r, st[r -- sk, val]), st[r -- _type] .type ≤ ty, 0 ≤ i, 0 < st[r -- _length] .intval ⊦ i ' = sk, sk = _length, sk = _type, r0 = st[r -- sk] .refval, val .refval = r0, r = r0, r = jvmref, r0 ∈ refs1, dups(refs1), r ∈ refs1, validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 45:
⊦ ¬ r ∈ refs → (validrefs(str, refs, ty, st[r -- sk, val]) ↔ validrefs(str, refs, ty, st))

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: validrefs-put-notin antecedent: succedent: ¬ r ∈ refs → ( validrefs(str, refs, ty, st[r -- sk, val]) ↔ validrefs(str, refs, ty, st)) substlist: [val, sk, r, st, ty, refs, str] → [val, sk, r, st, st[r -- _type] .type .type, r0 ' + refs1, str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((0, 0, 2)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : list, references, in-01, ⊦ r ≠ r0 → (r ∈ r0 ' + refs ↔ r ∈ refs)], [CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (val, sk, r, st, st[r -- _type] .type .type, r0 ' + refs1, str)]]