Nuprl Lemma : itermSubtract?_wf

[v:int_term()]. (itermSubtract?(v) ∈ 𝔹)


Proof




Definitions occuring in Statement :  itermSubtract?: itermSubtract?(v) int_term: int_term() bool: 𝔹 uall: [x:A]. B[x] member: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T ext-eq: A ≡ B and: P ∧ Q subtype_rel: A ⊆B all: x:A. B[x] implies:  Q bool: 𝔹 unit: Unit it: btrue: tt uiff: uiff(P;Q) uimplies: supposing a sq_type: SQType(T) guard: {T} eq_atom: =a y ifthenelse: if then else fi  itermConstant: "const" itermSubtract?: itermSubtract?(v) pi1: fst(t) bfalse: ff exists: x:A. B[x] prop: or: P ∨ Q bnot: ¬bb assert: b false: False itermVar: vvar itermAdd: left (+) right itermSubtract: left (-) right itermMultiply: left (*) right itermMinus: "-"num
Lemmas referenced :  int_term-ext eq_atom_wf bool_wf eqtt_to_assert assert_of_eq_atom subtype_base_sq atom_subtype_base bfalse_wf eqff_to_assert equal_wf bool_cases_sqequal bool_subtype_base assert-bnot neg_assert_of_eq_atom btrue_wf int_term_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut introduction extract_by_obid promote_hyp sqequalHypSubstitution productElimination thin hypothesis_subsumption hypothesis hypothesisEquality applyEquality sqequalRule isectElimination tokenEquality lambdaFormation unionElimination equalityElimination equalityTransitivity equalitySymmetry independent_isectElimination instantiate cumulativity atomEquality dependent_functionElimination independent_functionElimination because_Cache dependent_pairFormation voidElimination

Latex:
\mforall{}[v:int\_term()].  (itermSubtract?(v)  \mmember{}  \mBbbB{})



Date html generated: 2017_04_14-AM-08_57_01
Last ObjectModification: 2017_02_27-PM-03_40_35

Theory : omega


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