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Proof step 42 from proof refine-remap (previous step)

m < # avols0[default-volid], ebm-cons(avols0), ebm-vol-inv(abs(avols0[default-volid])), default-volid ∈ avols0 ⊦ mapped(mkbuf(0)) = abs(avols0[default-volid][m, mapped(emptyleb, 0)])[m]

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ebm-vol-abs name: abs-at seq: ⊦ n < # evol → abs(evol)[n] = abs(evol[n]) subst: [n, evol] → [m, avols0[default-volid][m, mapped(emptyleb, 0)]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m < # evol → evol[m, leb][m] = leb; (s)% ⊦ abs(mapped(buf, n)) = mapped(subarray(buf, 0, n)); (s)% ⊦ subarray(buf, n, 0) = mkbuf(0); (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)% ⊦ # evol[n, leb] = # evol; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: m, avols0[default-volid][m, mapped(emptyleb, 0)]