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Proof step 12 from proof refine-remap (previous step)

avol = abs(avols0[default-volid]), avols = avols0[v, avols0[v][m, unmapped]], v = default-volid, m < # avols0[default-volid], m < # avols0[v], ebm-cons(avols0), ebm-vol-inv(abs(avols0[default-volid])), default-volid ∈ avols0, v ∈ avols0 ⊦ ⟪ebm_map#(default-volid, m; avols; err)⟫ ⟨ebm_avol_remap#(m; avol; err0)⟩ (avol = abs(avols[default-volid]) ∧ err = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
avols = avols0[default-volid, avols0[default-volid][m, unmapped]], m < # avols0[default-volid], ebm-cons(avols0), ebm-vol-inv(abs(avols0[default-volid])), default-volid ∈ avols0 ⊦ ⟪ebm_map#(default-volid, m; avols; err)⟫ ⟨avol := abs(avols0[default-volid]); ebm_avol_remap#(m; avol; err0)⟩ (avol = abs(avols[default-volid]) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic