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Proof step 3 from proof pos-range (previous step)

∀ char. # str0 < pos(char, str0) → pos(char, str0) = 0, #(char0 + str0) < pos(char, char0 + str0) ⊦ pos(char, char0 + str0) = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
# str0 + 1 < pos(char, char0 ' + str0), ∀ char. # str0 < pos(char, str0) → pos(char, str0) = 0 ⊦ pos(char, char0 ' + str0) = 0

Rule argument

Additional information

Used simplifier rules: Length-rec: ⊦ #(char ' + str) = # str + 1;%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%assoc: ⊦ (str1 + str2) + str3 = str1 + str2 + str3; from specification string-append%chartostring-01: ⊦ char + str = char ' + str; from specification string-append