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Proof step 35 from proof validrefs-nodups (previous step)

refs .last = jvmref, (r ' + refs4) .last = jvmref, validrefs(str, (r ' + refs1) + r0 ' + refs, ty, st), validrefs(str, r ' + refs1 + r0 ' + refs0 + r0 ' + refs, ty, st), refs4 ⊆ (r ' + refs1) + r0 ' + refs, validrefs(str, r ' + refs4, ty, st), ∀ st, ty, str, refs3. # refs3 < # (r + (refs1 + (r0 + (refs0 + (r0 + refs))))) → ( validrefs(str, refs3, ty, st) ∧ refs3 ≠ [] ∧ refs3 .last = jvmref → (∃ refs1. validrefs(str, refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref ∧ refs3 .first = refs1 .first ∧ ¬ dups(refs1) ∧ refs1 ⊆ refs3)) ⊦ r = r0, refs = [], r ∈ refs1, r ∈ refs0, r ∈ refs, dups(refs4), r ∈ refs4, ∃ refs3. validrefs(str, refs3, ty, st) ∧ refs3 ≠ [] ∧ refs3 .last = jvmref ∧ r = refs3 .first ∧ ¬ dups(refs3) ∧ refs3 ⊆ refs3 .first ' + refs1 + r0 ' + refs0 + r0 ' + refs

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 28:
⊦ validrefs(str, jvmref ', ty, st)
Proof step 29:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []
Proof step 34:
refs .last = jvmref, (r ' + refs4) .last = jvmref, validrefs(str, (r ' + refs1) + r0 ' + refs, ty, st), validrefs(str, r ' + refs1 + r0 ' + refs0 + r0 ' + refs, ty, st), refs4 ⊆ (r ' + refs1) + r0 ' + refs, validrefs(str, r ' + refs4, ty, st), ∀ st, ty, str, refs3. # refs3 < # (r + (refs1 + (r0 + (refs0 + (r0 + refs))))) → ( validrefs(str, refs3, ty, st) ∧ refs3 ≠ [] ∧ refs3 .last = jvmref → (∃ refs1. validrefs(str, refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref ∧ refs3 .first = refs1 .first ∧ ¬ dups(refs1) ∧ refs1 ⊆ refs3)) ⊦ refs4 = [], r = r0, refs = [], r ∈ refs1, r ∈ refs0, r ∈ refs, dups(refs4), r ∈ refs4, ∃ refs3. validrefs(str, refs3, ty, st) ∧ refs3 ≠ [] ∧ refs3 .last = jvmref ∧ r = refs3 .first ∧ ¬ dups(refs3) ∧ refs3 ⊆ refs3 .first ' + refs1 + r0 ' + refs0 + r0 ' + refs

Rule argument

[fma-arg: refs4 = []]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refs + [] = refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' .last = r], [CSIMPSEQ : ⊦ [] ⊆ refs], [CSIMPSEQ : ⊦ ¬ dups([])], [CSIMPSEQ : ⊦ ¬ r ∈ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ r ' ≠ []])], [EXTRAFMAS : (refs4 = [])]]