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Proof step 78 from proof validrefs-put-badclassfield (previous step)

is_classtype(st[r0 -- _type] .type), validrefs(str, r ' + r1 ' + refs, ty, st[r0 -- fs ', val]), ∀ str0, ty0, st0, fs0, r2, val0. ¬ validrefs(str0, r1 ' + refs, ty0, st0) ∧ ¬ junkref(str0, r1, st0) ∧ fs0 ' ≠ _type ∧ is_classtype(st0[r2 -- _type] .type) ∧ ¬ fs0 ' ∈ instfields(st0[r2 -- _type] .type .class) → ¬ validrefs(str0, r1 ' + refs, ty0, st0[r2 -- fs0 ', val0]) ⊦ fs ' = _type, dups((r1 ' + refs) .butlast), r ∈ (r1 ' + refs) .butlast, fs ' ∈ instfields(st[r0 -- _type] .type .class), junkref(str, r, st), validrefs(str, r ' + r1 ' + refs, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → ¬ validrefs(str, r ' + refs, ty, st)
Proof step 77:
¬ (r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st[r0 -- fs ', val]) ∨ ¬ (st[r0 -- fs ', val][r -- _type]) .type ≤ ty)), is_classtype(st[r0 -- _type] .type), validrefs(str, r ' + r1 ' + refs, ty, st[r0 -- fs ', val]), ∀ str0, ty0, st0, fs0, r2, val0. ¬ validrefs(str0, r1 ' + refs, ty0, st0) ∧ ¬ junkref(str0, r1, st0) ∧ fs0 ' ≠ _type ∧ is_classtype(st0[r2 -- _type] .type) ∧ ¬ fs0 ' ∈ instfields(st0[r2 -- _type] .type .class) → ¬ validrefs(str0, r1 ' + refs, ty0, st0[r2 -- fs0 ', val0]) ⊦ fs ' = _type, dups((r1 ' + refs) .butlast), r ∈ (r1 ' + refs) .butlast, fs ' ∈ instfields(st[r0 -- _type] .type .class), junkref(str, r, st), validrefs(str, r ' + r1 ' + refs, ty, st)

Rule argument

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

Additional information

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