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Proof step 10 from proof validrefs-nopathex (previous step)

validrefs(str, r ' + refs, ty, st), ∃ refs0, refs1. refs = refs0 + r0 ' + refs1 ∧ ¬ r0 ∈ refs0, validrefs(str, r ' + refs, st[r -- _type] .type, st) ⊦ ∃ refs0. refs0 ≠ [] ∧ refs0 .first = r ∧ refs0 .last = r0 ∧ validrefs(str, refs0, st[refs0 .first -- _type] .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
validrefs(str, r ' + refs1 + r0 ' + refs0, ty, st), validrefs(str, r ' + refs1 + r0 ' + refs0, st[r -- _type] .type, st) ⊦ r0 ∈ refs1, ∃ refs0. refs0 ≠ [] ∧ refs0 .first = r ∧ refs0 .last = r0 ∧ validrefs(str, refs0, st[refs0 .first -- _type] .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]