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Proof step 79 from proof validrefs-put-badclassfield (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 78:
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

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []], [CSIMPSEQ : ⊦ dups(r ' + refs) ↔ dups(refs) ∨ r ∈ refs], [CSIMPSEQ : ⊦ (refs + r ' + refs0) .butlast = refs + (r ' + refs0) .butlast], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]