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Proof step 71 from proof validrefs-put-array-badindex (previous step)

i < 0, ∀ i0, str0, ty0, st0, r1, val0. ¬ 0 ≤ i0 → (validrefs(str0, refs0, ty0, st0[r1 -- i0 ', val0]) ↔ validrefs(str0, refs0, ty0, st0)) ⊦ validrefs(str, r0 ' + refs0, ty, st[r -- i ', val]) ↔ validrefs(str, r0 ' + refs0, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → ¬ validrefs(str, r ' + refs, ty, st)
Proof step 67:
¬ (r0 ≠ jvmref ∧ (¬ is_valid_ref(str, r0, st) ∨ ¬ st[r0 -- _type] .type ≤ ty)), i < 0, ∀ i0, str0, ty0, st0, r1, val0. ¬ 0 ≤ i0 → (validrefs(str0, refs0, ty0, st0[r1 -- i0 ', val0]) ↔ validrefs(str0, refs0, ty0, st0)) ⊦ validrefs(str, r0 ' + refs0, ty, st[r -- i ', val]) ↔ validrefs(str, r0 ' + refs0, ty, st)
Proof step 70:
r0 ≠ jvmref ∧ (¬ is_valid_ref(str, r0, st) ∨ ¬ st[r0 -- _type] .type ≤ ty), i < 0, ∀ i0, str0, ty0, st0, r1, val0. ¬ 0 ≤ i0 → (validrefs(str0, refs0, ty0, st0[r1 -- i0 ', val0]) ↔ validrefs(str0, refs0, ty0, st0)) ⊦ validrefs(str, r0 ' + refs0, ty, st[r -- i ', val]) ↔ false

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: validrefs-is-junk antecedent: succedent: r ≠ jvmref ∧ ( ¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → ¬ validrefs(str, r ' + refs, ty, st) substlist: [st, ty, refs, r, str] → [st, ty, refs0, r0, str] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 0, 1, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, refs0, r0, str)]]