Commit 6d9c66b4 authored by MARCHE Claude's avatar MARCHE Claude

test of ceil function

parent f61e99e7
theory Ceil
use import real.Real
use import real.RealInfix
use import real.Truncate
goal ceil_obvious: ceil 0.1 = 1
lemma unity:
forall b: real. b > 0.0 -> b = 1.0 *. b
lemma unity2:
forall b: real. b > 0.0 -> b /. b = (1.0 *. b) /. b
lemma perm_div:
forall a b:real. a > 0.0 /\ b > 0.0 -> (a *. b) /. b = a *. (b /. b)
lemma perm_div2:
forall a b:real. a > 0.0 /\ b > 0.0 -> a *. b /. b = a /. b *. b
lemma div_mult_perm:
forall b: real. b > 0.0 -> (1.0 /. b) *. b = (1.0 *. b) /. b
lemma b_div_b_is_one:
forall b: real. b > 0.0 -> 1.0 = b /. b
lemma inverse_inverse_is_same:
forall b: real. b > 0.0 -> 1.0 = (1.0 /. b) *. b
lemma inverse_bigger_zero:
forall b: real. b > 0.0 -> 1.0 /. b > 0.0
lemma div_equals_mult_w_inverse:
forall a b:real. b > 0.0 -> a /. b = a *. (1.0 /. b)
lemma mult_bigger_zero:
forall a b: real. a > 0.0 /\ b > 0.0 -> a *. b > 0.0
goal ceil_never_zero:
forall a b: real. a > 0.0 /\ b > 0.0 -> ceil (a /. b) <> 0
end
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