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Proof step 37 from proof pathexplus-pathex (previous step)

¬ ( (r ' + refs) .last ≠ jvmref ∧ (¬ is_valid_ref(str, (r ' + refs) .last, st) ∨ ¬ st[(r ' + refs) .last -- _type] .type ≤ st[(r ' + refs) .last -- _type] .type)), validrefs(str, r ' + refs, mkclasstype(`java.lang.Object' .class), st), validrefs(str, r ' + refs + r0 ', mkclasstype(`java.lang.Object' .class), st), is_valid_ref(str, r, st), validrefs(str, (r ' + refs) .last ' + r0 ', st[(r ' + refs) .last -- _type] .type, st) ⊦ r = r0, r = jvmref, step∃(str, (r ' + refs) .last, r0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
⊦ ¬ is_valid_ref(str, r, st) → (validrefs(str, r ' + refs, ty, st) ↔ r = jvmref ∧ refs = [])
Proof step 36:
validrefs(str, r ' + refs, mkclasstype(`java.lang.Object' .class), st), validrefs(str, r ' + refs + r0 ', mkclasstype(`java.lang.Object' .class), st), is_valid_ref(str, r, st), validrefs(str, (r ' + refs) .last ' + r0 ', st[(r ' + refs) .last -- _type] .type, st), is_valid_ref(str, (r ' + refs) .last, st) ⊦ r = r0, r = jvmref, step∃(str, (r ' + refs) .last, r0, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ty ≤ ty])]]