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Proof step 48 from proof pathexplus-pathex (previous step)

¬ (r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ mkclasstype(`java.lang.Object' .class))), validrefs(str, r ' + refs1, mkclasstype(`java.lang.Object' .class), st) ⊦ refs1 = [], r = refs1 .last, validrefs(str, r ' + refs1 .butlast, mkclasstype(`java.lang.Object' .class), st) ∧ step∃(str, (r ' + refs1 .butlast) .last, refs1 .last, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []
Proof step 5:
⊦ ¬ is_valid_ref(str, r, st) → (validrefs(str, r ' + refs, ty, st) ↔ r = jvmref ∧ refs = [])
Proof step 47:
validrefs(str, r ' + refs1, mkclasstype(`java.lang.Object' .class), st), is_valid_ref(str, r, st) ⊦ refs1 = [], r = refs1 .last, r = jvmref, validrefs(str, r ' + refs1 .butlast, mkclasstype(`java.lang.Object' .class), st) ∧ step∃(str, (r ' + refs1 .butlast) .last, refs1 .last, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ is_valid_ref(str, r, st) ∧ r ≠ jvmref → st[r -- _type] .type ≤ mkclasstype (`java.lang.Object' .class)])]]