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Proof step 8 from proof prepost-decode-orphans (previous step)

# buf = # orphans1 * ENCODED_NAT_SIZE, err = ESUCCESS, m = 0, m0 = n, n = # orphans1, orphans0 = ∅, is-encoded(orphans1, buf) ⊦ ⟪while err = ESUCCESS ∧ m0 ≠ 0 do {/* (prepost-decode-orphans : invariant (err = ESUCCESS ∨ ⌊err⌋ ) ∧ m + m0 * ENCODED_NAT_SIZE = # buf ∧ ( err = ESUCCESS → (∃ orphans. is-encoded(orphans0, subarray(buf, 0, m)) ∧ is-encoded(orphans, subarray(buf, m, # buf - m)) ∧ orphans ∩ orphans0 = ∅)) wfbound m0) */; let n = ?, m0 = ? in {decode_nat#(m, buf; n, m0; err); if err = ESUCCESS then orphans0 := orphans0 ++ n; m := m + ENCODED_NAT_SIZE}; m0 := m0 - 1}⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → orphans0 = orphans1))

Heuristic annotation applied rule annotation right

And obtained the following new goals

Proof step 9:
# buf = # orphans1 * ENCODED_NAT_SIZE, m + m0 * ENCODED_NAT_SIZE = # buf, err = ESUCCESS, err0 = ESUCCESS, m0 = m1, m2 = 0, m3 = n, n = # orphans1, orphans2 = ∅, is-encoded(orphans1, buf), err = ESUCCESS → (∃ orphans. is-encoded(orphans0, subarray(buf, 0, m)) ∧ is-encoded(orphans, subarray(buf, m, # buf - m)) ∧ orphans ∩ orphans0 = ∅), err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟪let n = ?, m0 = ? in {decode_nat#(m, buf; n, m0; err); if err = ESUCCESS then orphans0 := orphans0 ++ n; m := m + ENCODED_NAT_SIZE}; m0 := m0 - 1⟫ ( ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ m + m0 * ENCODED_NAT_SIZE = # buf ∧ ( err = ESUCCESS → (∃ orphans. is-encoded(orphans0, subarray(buf, 0, m)) ∧ is-encoded(orphans, subarray(buf, m, # buf - m)) ∧ orphans ∩ orphans0 = ∅))) ∧ m0 < m1), m0 = 0

Rule argument

rule: invariant right arg: bound: m0 inv: (err = ESUCCESS ∨ ⌊err⌋ ) ∧ m + m0 * ENCODED_NAT_SIZE = # buf ∧ ( err = ESUCCESS → (∃ orphans. is-encoded(orphans0, subarray(buf, 0, m)) ∧ is-encoded (orphans, subarray(buf, m, # buf - m)) ∧ orphans ∩ orphans0 = ∅)) fmapos: right 1 pos: right 1

Additional information

Used simplifier rules: ⊦ 0 * n = 0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ is-encoded(ns0, buf) → (is-encoded(ns1, buf) ↔ ns0 = ns1); (s)% ⊦ subarray(buf, n, 0) = mkbuf(0); (s)% ⊦ is-encoded(∅, buf) ↔ buf = mkbuf(0); (s)% ⊦ m - 0 = m; (s)% ⊦ ns ∩ ∅ = ∅; (s)%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set] Used formulas: (err = ESUCCESS ∨ ⌊err⌋ ) ∧ m + m0 * ENCODED_NAT_SIZE = # buf ∧ ( err = ESUCCESS → (∃ orphans. is-encoded(orphans0, subarray(buf, 0, m)) ∧ is-encoded(orphans, subarray(buf, m, # buf - m)) ∧ orphans ∩ orphans0 = ∅)), m0 = m0