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Proof step 55 from proof disjoint-nojunk-newref-subset-01 (previous step)

(r1 ' + refs0) .last = (r ' + refs1) .last, r1 ∈ st, st ⊆ st1, newref(r, st), validrefs(str, r ' + refs1, st1[r -- _type] .type, st1), validrefs(str, r1 ' + refs0, st[r1 -- _type] .type, st1), r1 -- _type ∈ st ⊦ r = r1, r = jvmref, (r ' + refs1) .last = jvmref, path∃(str, r, (r ' + refs1) .last, st1), junkref(str, r1, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 47:
⊦ ¬ path∃(str, r, r0, st) ∧ r0 ∈ refs → ¬ validrefs(str, r ' + refs, ty, st)
Proof step 54:
¬ (¬ path∃(str, r, (r ' + refs1) .last, st1) ∧ (r ' + refs1) .last ∈ refs1), (r1 ' + refs0) .last = (r ' + refs1) .last, r1 ∈ st, st ⊆ st1, newref(r, st), validrefs(str, r ' + refs1, st1[r -- _type] .type, st1), validrefs(str, r1 ' + refs0, st[r1 -- _type] .type, st1), r1 -- _type ∈ st ⊦ r = r1, r = jvmref, (r ' + refs1) .last = jvmref, path∃(str, r, (r ' + refs1) .last, st1), junkref(str, r1, st)

Rule argument

[x0lemmaarg: spec-name: cyclic instance-name: lemma-name: validrefs-nopathex antecedent: succedent: ¬ path∃(str, r, r0, st) ∧ r0 ∈ refs → ¬ validrefs(str, r ' + refs, ty, st) substlist: [str, r, r0, st, refs, ty] → [str, r, (r ' + refs1) .last, st1, refs1, st1[r -- _type] .type] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 4)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str, r, (r ' + refs1) .last, st1, refs1, st1[r -- _type] .type)]]