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Proof step 132 from proof hasSharing-dd-help (previous step)

validrefs(str, r ' + refs + r1 ', st[r -- _type] .type, st), validrefs(str, r2 ' + refs2 + r0 ', st[r2 -- _type] .type, st), validrefs(str, r1 ' + refs1 + r0 ', st[r1 -- _type] .type, st), path∃(str, r, r2, st) ⊦ r2 = r1, r0 = jvmref, r1 = r0, path∃(str, r1, r2, st), path∃(str, r2, r1, st), hasSharing(r, st)

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 9:
⊦ validrefs(str, refs + r ', ty, st) ∧ validrefs(str, r ' + refs0, ty0, st) → validrefs(str, refs + r ' + refs0, ty, st)
Proof step 131:
validrefs(str, (r ' + refs) + r1 ', st[r -- _type] .type, st) ∧ validrefs(str, r1 ' + refs1 + r0 ', st[r1 -- _type] .type, st) → validrefs(str, (r ' + refs) + r1 ' + refs1 + r0 ', st[r -- _type] .type, st), validrefs(str, r ' + refs + r1 ', st[r -- _type] .type, st), validrefs(str, r2 ' + refs2 + r0 ', st[r2 -- _type] .type, st), validrefs(str, r1 ' + refs1 + r0 ', st[r1 -- _type] .type, st), path∃(str, r, r2, st) ⊦ r2 = r1, r0 = jvmref, r1 = r0, path∃(str, r1, r2, st), path∃(str, r2, r1, st), hasSharing(r, st)

Rule argument

[speclemmaarg: , validrefs(str, refs + r ', ty, st) ∧ validrefs(str, r ' + refs0, ty0, st) → validrefs(str, refs + r ' + refs0, ty, st) ,[str, refs, r, ty, st, refs0, ty0] → [str, r ' + refs, r1, st[r -- _type] .type, st, refs1 + r0 ', st[r1 -- _type] .type] ,F ,cyclic , ,validrefs-append ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str, r ' + refs, r1, st[r -- _type] .type, st, refs1 + r0 ', st[r1 -- _type] .type)]]