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Proof step 11 from proof pathex-def-simple (previous step)

validrefs(str, r ' + refs1, st[r -- _type] .type, st) ⊦ validrefs(str, r ' + refs1, mkclasstype(`java.lang.Object' .class), st), st[r -- _type] .type ≤ mkclasstype(`java.lang.Object' .class)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → ¬ validrefs(str, r ' + refs, ty, st)
Proof step 9:
⊦ validrefs(str, jvmref ' + refs, ty, st) ↔ refs = []
Proof step 10:
⊦ ¬ is_valid_ref(str, r, st) → (validrefs(str, r ' + refs, ty, st) ↔ r = jvmref ∧ refs = [])

Rule argument

[crewrite-arg: validrefs-is-junk , F , [st, ty, refs, r, str] → [st, st[r -- _type] .type, refs1, r, str] ]

Additional information

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