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Proof step 77 from proof validrefs-put-notin-01 (previous step)

r ∈ st, okval(st[r -- fs '], fs .type), r -- fs ' ∈ st, okval(val, fs .type), ∀ r2, fs0, val0, st0, str0, r3, ty0. ¬ r2 ∈ acc ∧ fs0 ' ≠ _type ∧ fs0 ' ≠ _length ∧ okval(val0, fs0 .type) ∧ r2 -- fs0 ' ∈ st0 ∧ okval(st0[r2 -- fs0 '], fs0 .type) → (validrefs(str0, acc + r3 ', ty0, st0[r2 -- fs0 ', val0]) ↔ validrefs(str0, acc + r3 ', ty0, st0)) ⊦ r1 = jvmref, r = r1, validrefs(str, (r1 ' + acc) + r0 ', ty, st[r -- fs ', val]) ↔ validrefs(str, (r1 ' + acc) + r0 ', ty, st), fs ' = _type, fs ' = _length, r ∈ acc

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → ¬ validrefs(str, r ' + refs, ty, st)
Proof step 72:
¬ (r1 ≠ jvmref ∧ (¬ is_valid_ref(str, r1, st[r -- fs ', val]) ∨ ¬ (st[r -- fs ', val][r1 -- _type]) .type ≤ ty)), r ∈ st, okval(st[r -- fs '], fs .type), r -- fs ' ∈ st, okval(val, fs .type), ∀ r2, fs0, val0, st0, str0, r3, ty0. ¬ r2 ∈ acc ∧ fs0 ' ≠ _type ∧ fs0 ' ≠ _length ∧ okval(val0, fs0 .type) ∧ r2 -- fs0 ' ∈ st0 ∧ okval(st0[r2 -- fs0 '], fs0 .type) → (validrefs(str0, acc + r3 ', ty0, st0[r2 -- fs0 ', val0]) ↔ validrefs(str0, acc + r3 ', ty0, st0)) ⊦ r1 = jvmref, r = r1, validrefs(str, (r1 ' + acc) + r0 ', ty, st[r -- fs ', val]) ↔ validrefs(str, (r1 ' + acc) + r0 ', ty, st), fs ' = _type, fs ' = _length, r ∈ acc
Proof step 76:
r1 ≠ jvmref ∧ (¬ is_valid_ref(str, r1, st[r -- fs ', val]) ∨ ¬ (st[r -- fs ', val][r1 -- _type]) .type ≤ ty), r ∈ st, okval(st[r -- fs '], fs .type), r -- fs ' ∈ st, okval(val, fs .type), ∀ r2, fs0, val0, st0, str0, r3, ty0. ¬ r2 ∈ acc ∧ fs0 ' ≠ _type ∧ fs0 ' ≠ _length ∧ okval(val0, fs0 .type) ∧ r2 -- fs0 ' ∈ st0 ∧ okval(st0[r2 -- fs0 '], fs0 .type) → (validrefs(str0, acc + r3 ', ty0, st0[r2 -- fs0 ', val0]) ↔ validrefs(str0, acc + r3 ', ty0, st0)) ⊦ r1 = jvmref, r = r1, false ↔ validrefs(str, (r1 ' + acc) + r0 ', ty, st), fs ' = _type, fs ' = _length, r ∈ acc

Rule argument

[crewrite-arg: validrefs-is-junk , F , [st, ty, refs, r, str] → [st[r -- fs ', val], ty, acc + r0 ', r1, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st[r -- fs ', val], ty, acc + r0 ', r1, str)]]