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Proof step 39 from proof refine-remap (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 40:
⊦ m ≠ n → avol[n, aleb][m] = avol[m]
Proof step 41:
n = m, n < # avols0[default-volid], m < # avols0[default-volid], ebm-cons(avols0), ebm-vol-inv(abs(avols0[default-volid])), default-volid ∈ avols0 ⊦ abs(avols0[default-volid])[m, mapped(mkbuf(0))][n] = abs(avols0[default-volid][m, mapped(emptyleb, 0)])[n]
Proof step 44:
n < # avols0[default-volid], m < # avols0[default-volid], ebm-cons(avols0), ebm-vol-inv(abs(avols0[default-volid])), default-volid ∈ avols0 ⊦ abs(avols0[default-volid])[n] = abs(avols0[default-volid][m, mapped(emptyleb, 0)])[n], n = m

Rule argument

spec: array, inst: avolume name: Put-other seq: ⊦ m ≠ n → avol[n, aleb][m] = avol[m] subst: [m, aleb, n, avol] → [n, mapped(mkbuf(0)), m, abs(avols0[default-volid])] flags: <all paths>

Additional information

Used terms: n, mapped(mkbuf(0)), m, abs(avols0[default-volid])