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Proof step 71 from proof disjoint-nojunk-newref-subset-01 (previous step)

st ⊆ st1, newref(r, st), ∀ r0. path∃(str, r, r0, st1) → newref(r0, st) ∨ r0 = jvmref ⊦ r = jvmref, disjoint(str, r1 ' + r ', st1), junkref(str, r1, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ disjoint(str, refs, st) ↔ ¬ (∃ refs1, refs2. refs1 ≠ [] ∧ refs2 ≠ [] ∧ refs1 .first ∈ refs ∧ refs2 .first ∈ refs ∧ refs1 .first ≠ refs2 .first ∧ refs1 .last = refs2 .last ∧ refs1 .last ≠ jvmref ∧ validrefs(str, refs1, st[refs1 .first -- _type] .type, st) ∧ validrefs(str, refs2, st[refs2 .first -- _type] .type, st))
Proof step 70:
st ⊆ st1, newref(r, st), ∀ r0. path∃(str, r, r0, st1) → newref(r0, st) ∨ r0 = jvmref ⊦ r = jvmref, ∀ refs1, refs2. ¬ ( refs1 ≠ [] ∧ refs2 ≠ [] ∧ refs1 .first ∈ r1 ' + r ' ∧ refs2 .first ∈ r1 ' + r ' ∧ refs1 .first ≠ refs2 .first ∧ refs1 .last = refs2 .last ∧ refs1 .last ≠ jvmref ∧ validrefs(str, refs1, st1[refs1 .first -- _type] .type, st1) ∧ validrefs(str, refs2, st1[refs2 .first -- _type] .type, st1)), junkref(str, r1, st)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: disjoint-def antecedent: succedent: disjoint(str, refs, st) ↔ ¬ (∃ refs1, refs2. refs1 ≠ [] ∧ refs2 ≠ [] ∧ refs1 .first ∈ refs ∧ refs2 .first ∈ refs ∧ refs1 .first ≠ refs2 .first ∧ refs1 .last = refs2 .last ∧ refs1 .last ≠ jvmref ∧ validrefs (str, refs1, st[refs1 .first -- _type] .type, st) ∧ validrefs (str, refs2, st[refs2 .first -- _type] .type, st)) substlist: [st, refs, str] → [st1, r1 ' + r ', str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st1, r1 ' + r ', str)]]