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Proof step 7 from proof replaylog-prog (previous step)

ax1 = adr + ax0, err = ESUCCESS, ri = replay-log(ax, fs, ri1), replay-safe(ax + ax1, fs, ri1), replay-safe(ax1, fs, replay-log(ax, fs, ri1)) ⊦ ⟪aubifs_replayone#(adr, fi, ro, fo, fs, log, boolvar; err, ri); ax2 := ax0⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → (∃ ax3. ax + ax1 = ax3 + ax2 ∧ replay-safe(ax2, fs, replay-log(ax3, fs, ri1)) ∧ ri = replay-log(ax3, fs, ri1))) ∧ # ax2 < # ax1), ax1 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
err = ESUCCESS, ri = replay-log(ax, fs, ri1), node-cons(fs[adr].key, fs[adr]), replay-safe(ax0, fs, replay-one(adr, fs[adr], replay-log(ax, fs, ri1))), replay-safe(ax + adr ' + ax0, fs, ri1), adr ∈ fs, ¬ adr ∈ replay-log(ax, fs, ri1) ⊦ ⟪aubifs_replayone#(adr, fi, ro, fo, fs, log, boolvar; err, ri); ax2 := ax0⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → (∃ ax1. ax + adr ' + ax0 = ax1 + ax2 ∧ replay-safe(ax2, fs, replay-log(ax1, fs, ri1)) ∧ ri = replay-log(ax1, fs, ri1))) ∧ ¬ # ax0 < # ax2)

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m +1 = m + 1; (s)% ⊦ #(adr ' + ax) = (# ax)+1; (s)%⊦ replay-safe(adr ' + log, fs, ri) ↔ adr ∈ fs ∧ ¬ adr ∈ ri ∧ node-cons(fs[adr].key, fs[adr]) ∧ replay-safe(log, fs, replay-one(adr, fs[adr], ri)); (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ adr ' + ax ≠ []; (s)% ⊦ adr + ax = adr ' + ax; (s)