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Proof step 73 from proof validrefs-put-notin-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → ¬ validrefs(str, r ' + refs, ty, st)
Proof step 72:
¬ (r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st[r -- sk, val]) ∨ ¬ (st[r -- sk, val][r -- _type]) .type ≤ ty)), is_valid_ref(str, r, st), st[r -- _type] .type ≤ ty, is_valid_ref(str, r, st[r -- sk, val]) ⊦ r = r0, val .refval = r0, r0 = st[r -- sk] .refval, sk = _type, sk = _length, validrefs(str, r ' + r0 ' + refs1, ty, st[r -- sk, val]) ↔ validrefs(str, r ' + r0 ' + refs1, ty, st), r = jvmref, r ∈ refs1, dups(refs1), r0 ∈ refs1

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: validrefs-is-junk antecedent: succedent: r ≠ jvmref ∧ ( ¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → ¬ validrefs(str, r ' + refs, ty, st) substlist: [st, ty, refs, r, str] → [st[r -- sk, val], ty, r0 ' + refs1, r, str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 5, 1, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : javastore, , at-other-16, ⊦ sk ≠ sk0 → (st[r -- sk, val] [r0 -- sk0 ] ) = st[r0 -- sk0]], [CSIMPNAMEDSEQ : list, references, a, ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st[r -- sk, val], ty, r0 ' + refs1, r, str)]]