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Proof step 62 from proof refine-read (previous step)

avols[default-volid][m2] = mapped(buf0, n1), m2 < # avols[default-volid], ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), default-volid ∈ avols, m1 + n2 ≤ LEB_SIZE, n3 + n2 ≤ # buf2, m1 + n2 ≤ n1 + (LEB_SIZE - n1) ⊦ ∃ buf, n. mapped(buf0, n1) = mapped(buf, n)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 63:
LEB_SIZE = n0 + n1, avols[default-volid][m2] = mapped(buf0, n1), m2 < # avols[default-volid], ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), default-volid ∈ avols, m1 + n2 ≤ n1 + n0, n3 + n2 ≤ # buf2, m1 + n2 ≤ LEB_SIZE, n1 ≤ LEB_SIZE ⊦ ∃ buf, n. mapped(buf0, n1) = mapped(buf, n)

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [n1, LEB_SIZE, n0]

Additional information

Used simplifier rules: ⊦ v ∈ avols ∧ m < # avols[v] ∧ avols[v][m] = mapped(buf, n) ∧ ebm-cons(avols) → n ≤ LEB_SIZE; (ss)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n1, LEB_SIZE, n0