[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 4 from proof prepost-next2pot (previous step)

2exp-size(n) ⊦ ⟪while n < minsize do n := n * 2⟫ (2exp-size(n) ∧ minsize ≤ n)

User applied rule invariant right

And obtained the following new goals

Proof step 5:
n = n0, 2exp-size(n1), 2exp-size(n), n < minsize ⊦ ⟪n := n * 2⟫ (2exp-size(n) ∧ (n ≥ minsize ⊃ 0;minsize - n) < (n0 ≥ minsize ⊃ 0;minsize - n0))

Rule argument

bound: (n ≥ minsize ⊃ 0;minsize - n) inv: 2exp-size(n) fmapos: right 1

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss) Used formulas: 2exp-size(n), (n ≥ minsize ⊃ 0;minsize - n) = (n ≥ minsize ⊃ 0;minsize - n)