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Proof step 3 from proof junkref-put-nopathexplus-equiv (previous step)

junkrefs(str, r ' + refs0, st[r -- _type] .type, st[r0 -- sk, val]), ∀ val, sk, r0, st, r, str, refs. # refs < # refs0 → (junkrefs(str, r ' + refs, st[r -- _type] .type, st[r0 -- sk, val]) → sk = _type ∨ junkref(str, r, st) ∨ path∃+(str, r, r0, st)) ⊦ sk = _type, path∃+(str, r, r0, st), junkref(str, r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ¬ path∃+(str, r, r0, st) ∧ sk ≠ _type ∧ refs ≠ [] ∧ refs .first = r → (junkrefs(str, refs, ty, st[r0 -- sk, val]) ↔ junkrefs(str, refs, ty, st))

Rule argument

[crewrite-arg: junkrefs-put-nopathexplus-equiv , F , [str, r, r0, st, sk, refs, ty, val] → [str, (r ' + refs0) .first, r0, st, sk, r ' + refs0, st[r -- _type] .type, val] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ junkref(str, r, st) → ( junkrefs (str, r ' + refs0, st[r -- _type] .type, st) ↔ false)], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []])], [EXTRATERMS : (str, (r ' + refs0) .first, r0, st, sk, r ' + refs0, st[r -- _type] .type, val)]]