Nuprl Lemma : r2-det-identity

[p,q,r,t:ℝ^2].  (|pqr| (|tqr| |ptr| |pqt|))


Proof




Definitions occuring in Statement :  r2-det: |pqr| real-vec: ^n req: y radd: b uall: [x:A]. B[x] natural_number: $n
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T r2-det: |pqr| implies:  Q nat: le: A ≤ B and: P ∧ Q less_than': less_than'(a;b) false: False not: ¬A prop: real-vec: ^n int_seg: {i..j-} lelt: i ≤ j < k less_than: a < b squash: T true: True uiff: uiff(P;Q) uimplies: supposing a all: x:A. B[x] req_int_terms: t1 ≡ t2 top: Top
Lemmas referenced :  req_witness r2-det_wf radd_wf real-vec_wf false_wf le_wf rsub_wf rmul_wf lelt_wf itermSubtract_wf itermAdd_wf itermMultiply_wf itermVar_wf req-iff-rsub-is-0 real_polynomial_null int-to-real_wf real_term_value_sub_lemma real_term_value_add_lemma real_term_value_mul_lemma real_term_value_var_lemma real_term_value_const_lemma
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis independent_functionElimination dependent_set_memberEquality natural_numberEquality sqequalRule independent_pairFormation lambdaFormation isect_memberEquality because_Cache applyEquality imageMemberEquality baseClosed productElimination independent_isectElimination dependent_functionElimination approximateComputation lambdaEquality int_eqEquality intEquality voidElimination voidEquality

Latex:
\mforall{}[p,q,r,t:\mBbbR{}\^{}2].    (|pqr|  =  (|tqr|  +  |ptr|  +  |pqt|))



Date html generated: 2017_10_03-AM-11_42_30
Last ObjectModification: 2017_06_09-PM-01_55_23

Theory : reals


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