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Proof step 20 from proof disjoint-def-pathex (previous step)

(r2 ' + refs2) .last = (r3 ' + refs1) .last, r2 ∈ refs, r3 ∈ refs, validrefs(str, r2 ' + refs2, st[r2 -- _type] .type, st), validrefs(str, r3 ' + refs1, st[r3 -- _type] .type, st), ¬ path∃(str, r2, (r3 ' + refs1) .last, st) ∨ ¬ path∃(str, r3, (r3 ' + refs1) .last, st) ⊦ r2 = r3, (r3 ' + refs1) .last = jvmref

User applied rule case distinction

And obtained the following new goals

Proof step 14:
¬ path∃(str, r2, (r3 ' + refs1) .last, st), (r2 ' + refs2) .last = (r3 ' + refs1) .last, r2 ∈ refs, r3 ∈ refs, validrefs(str, r2 ' + refs2, st[r2 -- _type] .type, st), validrefs(str, r3 ' + refs1, st[r3 -- _type] .type, st) ⊦ r2 = r3, (r3 ' + refs1) .last = jvmref
Proof step 19:
¬ path∃(str, r3, (r3 ' + refs1) .last, st), (r2 ' + refs2) .last = (r3 ' + refs1) .last, r2 ∈ refs, r3 ∈ refs, validrefs(str, r2 ' + refs2, st[r2 -- _type] .type, st), validrefs(str, r3 ' + refs1, st[r3 -- _type] .type, st) ⊦ r2 = r3, (r3 ' + refs1) .last = jvmref

Rule argument

[CASEDARG : pos: left 6, ()]

Additional information

[[CONCRETESIMPRULES : ()]]