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Proof step 2 from proof lf-mapped-not-bad (previous step)

vols[v][m] = ⌜n⌝ , apebs[n] = mkpeb(aehdr, avhdr, buf, m0, boolvar), boolvar, m < # vols[v], valid-ebatbl(apebs, wlar, vols, n0), valid-wl(apebs, wlar), v ∈ vols ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
apebs[n] = mkpeb(aehdr, avhdr, buf, m0, true), vols[v][m] = ⌜n⌝ , avhdr.valid?, m < # vols[v], n < # apebs, valid-ebatbl(apebs, wlar, vols, n0), valid-wl(apebs, wlar), v ∈ vols ⊦

Rule argument

Additional information

Used simplifier rules: lf-mapped-valid-vidhdr: ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ ∧ valid-ebatbl(apebs, wlar, vols, n0) ∧ apebs[n] = mkpeb(aehdr, avhdr, buf, m0, boolvar) → avhdr.valid?;%lf-mapped-in-apebs: ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ ∧ valid-ebatbl(apebs, wlar, vols, n0) → n < # apebs;% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic