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Proof step 9 from proof prepost-restore-log (previous step)

log = abs-log(nx0, gstore2 ↓), elems(nx0 + nx1) ∩ ginval = ∅, nx1 ≠ [], inv(gstore2 \ ginval), elems(nx0 + nx1) ⊆ dom gstore2 ⊦ ⟪gjournal_remove_nonend_blocks#(nx1.head, fi0, fi, ginval, gstore2, gstore, nx, pmaxino, p_os, jvalid; log; err); nx := nx1.tail⟫ ((∃ nx3. nx0 + nx1 = nx3 + nx ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → log = abs-log(nx3, gstore2 ↓))) ∧ # nx < # nx1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
log = abs-log(nx0, gstore2 ↓), nx1 = n + nx2, elems(nx0 + nx1) ∩ ginval = ∅, inv(gstore2 \ ginval), elems(nx0 + nx1) ⊆ dom gstore2 ⊦ ⟪gjournal_remove_nonend_blocks#(n, fi0, fi, ginval, gstore2, gstore, nx, pmaxino, p_os, jvalid; log; err); nx := nx2⟫ ((∃ nx3. nx0 + nx1 = nx3 + nx ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → log = abs-log(nx3, gstore2 ↓))) ∧ # nx < # nx1), nx1 = []

Rule argument

spec: list-data, inst: nat-list-set name: elim-list-c seq: nx ≠ [] ⊦ n = nx.head ∧ nx0 = nx.tail ↔ nx = n + nx0 subst: [nx, n, nx0] → [nx1, n, nx2]

Additional information

Used simplifier rules: nx ≠ [] ⊦ n = nx.head ∧ nx0 = nx.tail ↔ nx = n + nx0; (elim) Used terms: nx1, n, nx2