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Proof step 6 from proof pathex-put-last (previous step)

validrefs(str, r ' + refs1 + r0 ', st[r -- _type] .type, st[r0 -- sk, val]) ⊦ sk = _type, r = r0, r ∈ refs1, dups(refs1), r0 ∈ refs1, junkref(str, r, st), r ' + refs1 + r0 ' ≠ [] ∧ (r ' + refs1 + r0 ') .first = r ∧ (r ' + refs1 + r0 ') .last = r0 ∧ ¬ dups(r ' + refs1 + r0 ') ∧ validrefs(str, r ' + refs1 + r0 ', st[(r ' + refs1 + r0 ') .first -- _type] .type, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
validrefs(str, r ' + refs1 + r0 ', st[r -- _type] .type, st[r0 -- sk, val]) ⊦ sk = _type, r = r0, r ∈ refs1, dups(refs1), r0 ∈ refs1, junkref(str, r, st), validrefs(str, r ' + refs1 + r0 ', st[r -- _type] .type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ dups(refs + r ') ↔ r ∈ refs ∨ dups(refs)], [CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPSEQ : ⊦ dups(r ' + refs) ↔ ¬ ¬ (r ∈ refs ∨ dups(refs))], [CSIMPSEQ : ⊦ (r ' + refs + r0 ') .last = r0], [CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []])]]