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Proof step 72 from proof validrefs-put-array-badindex (previous step)

∀ i, str, ty, st, r, val. i < 0 → (validrefs(str, refs0, ty, st[r -- i ', val]) ↔ validrefs(str, refs0, ty, st)), i < 0 ⊦ validrefs(str, r0 + refs0, ty, st[r -- i ', val]) ↔ validrefs(str, r0 + refs0, ty, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 71:
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)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPNAMEDSEQ : int-abs, , lels, ⊦ ¬ i < j ↔ j ≤ i], [CSIMPNAMEDSEQ : list, references, c, ⊦ r + refs = r ' + refs])]]