She’s so small and helpless, and we love her so much. “We had our first child, Amanda, three months ago. Where are you, Pookie? I’m home, and I’ve missed you so much.”
#Cambridge definition of lame crack#
It can be a name for a crack pipe that crackheads use to smoke their drugs. If someone is your “ Pookie,” they mean a great deal to you, and there would be a hole in your life without them around. The phrase can act as a pet name for your lover or partner, or it could be a pet name for your daughter or your pet poodle.
The expression “ Pookie” is a term of endearment for someone or something that you care about deeply in your life.
#Cambridge definition of lame update#
) " by ( simp add : succ_def mem_not_refl cons_fun_eq ) subsection ‹Function Updates› definition update :: " ⇒ i " where " update ( f, a, b ) ≡ λ x ∈ cons ( a, domain ( f ) ). x ∈ A ⟹ f ` x ∈ B ( x ) ⟧ ⟹ f ∈ Pi ( A, B ) " apply ( simp only : Pi_iff ) apply ( blast dest : function_apply_equality ) done (*Such functions arise in non-standard datatypes, ZF/ex/Ntree for instance*) lemma Pi_Collect_iff : " ( f ∈ Pi ( A, λ x.
c = " apply ( frule fun_is_rel ) apply ( blast dest : apply_equality ) done lemma function_apply_Pair : " ⟦ function ( f ) a ∈ domain ( f ) ⟧ ⟹ : f " apply ( simp add : function_def, clarify ) apply ( subgoal_tac " f ` a = y ", blast ) apply ( simp add : apply_def, blast ) done lemma apply_Pair : " ⟦ f ∈ Pi ( A, B ) a ∈ A ⟧ ⟹ : f " apply ( simp add : Pi_iff ) apply ( blast intro : function_apply_Pair ) done (*Conclusion is flexible - use rule_tac or else apply_funtype below!*) lemma apply_type : " ⟦ f ∈ Pi ( A, B ) a ∈ A ⟧ ⟹ f ` a ∈ B ( a ) " by ( blast intro : apply_Pair dest : fun_is_rel ) (*This version is acceptable to the simplifier*) lemma apply_funtype : " ⟦ f ∈ A -> B a ∈ A ⟧ ⟹ f ` a ∈ B " by ( blast dest : apply_type ) lemma apply_iff : " f ∈ Pi ( A, B ) ⟹ ⟨ a, b ⟩ : f ⟷ a ∈ A ∧ f ` a = b " apply ( frule fun_is_rel ) apply ( blast intro ! : apply_Pair apply_equality ) done (*Refining one Pi type to another*) lemma Pi_type : " ⟦ f ∈ Pi ( A, C ) ⋀ x. Sigmas and Pis are abbreviated as * or -> *) (*Weakening one function type to another see also Pi_type*) lemma fun_weaken_type : " ⟦ f ∈ A -> B B D " by ( unfold Pi_def, best ) subsection ‹Function Application› lemma apply_equality2 : " ⟦ ⟨ a, b ⟩ : f ⟨ a, c ⟩ : f f ∈ Pi ( A, B ) ⟧ ⟹ b = c " by ( unfold Pi_def function_def, blast ) lemma function_apply_equality : " ⟦ ⟨ a, b ⟩ : f function ( f ) ⟧ ⟹ f ` a = b " by ( unfold apply_def function_def, blast ) lemma apply_equality : " ⟦ ⟨ a, b ⟩ : f f ∈ Pi ( A, B ) ⟧ ⟹ f ` a = b " unfolding Pi_def apply ( blast intro : function_apply_equality ) done (*Applying a function outside its domain yields 0*) lemma apply_0 : " a ∉ domain ( f ) ⟹ f ` a = 0 " by ( unfold apply_def, blast ) lemma Pi_memberD : " ⟦ f ∈ Pi ( A, B ) c ∈ f ⟧ ⟹ ∃ x ∈ A.
x ∈ A' ⟹ B ( x ) = B' ( x ) ⟧ ⟹ Pi ( A, B ) = Pi ( A', B' ) " by ( simp add : Pi_def cong add : Sigma_cong ) (*Sigma_cong, Pi_cong NOT given to Addcongs: they causeįlex-flex pairs and the "Check your prover" error. ⟦ ⟨ x, y ⟩ : r : r ⟧ ⟹ y = y' ⟧ ⟹ function ( r ) " by ( simp add : function_def, blast ) (*Functions are relations*) lemma fun_is_rel : " f ∈ Pi ( A, B ) ⟹ f ⊆ Sigma ( A, B ) " by ( unfold Pi_def, blast ) lemma Pi_cong : " ⟦ A = A' ⋀ x. *) section ‹Functions, Function Spaces, Lambda-Abstraction› theory func imports equalities Sum begin subsection ‹The Pi Operator: Dependent Function Space› lemma subset_Sigma_imp_relation : " r ⊆ Sigma ( A, B ) ⟹ relation ( r ) " by ( simp add : relation_def, blast ) lemma relation_converse_converse : " relation ( r ) ⟹ converse ( converse ( r ) ) = r " by ( simp add : relation_def, blast ) lemma relation_restrict : " relation ( restrict ( r, A ) ) " by ( simp add : restrict_def relation_def, blast ) lemma Pi_iff : " f ∈ Pi ( A, B ) ⟷ function ( f ) ∧ f range ( f ) " by ( simp add : Pi_iff relation_def, blast ) lemma functionI : " ⟦ ⋀ x y y'. Author: Lawrence C Paulson, Cambridge University Computer Laboratory
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