Nuprl Lemma : cosine_wf

[x:ℝ]. (cosine(x) ∈ ℝ)


Proof




Definitions occuring in Statement :  cosine: cosine(x) real: uall: [x:A]. B[x] member: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T cosine: cosine(x) subtype_rel: A ⊆B all: x:A. B[x] so_lambda: λ2x.t[x] nat: ge: i ≥  decidable: Dec(P) or: P ∨ Q uimplies: supposing a satisfiable_int_formula: satisfiable_int_formula(fmla) exists: x:A. B[x] false: False implies:  Q not: ¬A top: Top and: P ∧ Q prop: nat_plus: + int_nzero: -o so_apply: x[s] nequal: a ≠ b ∈  guard: {T}
Lemmas referenced :  cosine-exists-ext all_wf exists_wf series-sum_wf int-rmul_wf int-rdiv_wf fact_wf nat_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermMultiply_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_mul_lemma int_term_value_var_lemma int_formula_prop_wf le_wf subtype_rel_sets less_than_wf nequal_wf nat_plus_properties intformeq_wf intformless_wf int_formula_prop_eq_lemma int_formula_prop_less_lemma equal-wf-base int_subtype_base rnexp_wf nat_wf pi1_wf_top real_wf equal_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule applyEquality thin instantiate extract_by_obid hypothesis lambdaEquality sqequalHypSubstitution hypothesisEquality isectElimination because_Cache dependent_set_memberEquality multiplyEquality natural_numberEquality setElimination rename dependent_functionElimination unionElimination independent_isectElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll setEquality lambdaFormation equalityTransitivity equalitySymmetry Error :applyLambdaEquality,  baseClosed independent_functionElimination productElimination independent_pairEquality axiomEquality

Latex:
\mforall{}[x:\mBbbR{}].  (cosine(x)  \mmember{}  \mBbbR{})



Date html generated: 2016_10_26-AM-09_25_36
Last ObjectModification: 2016_08_25-PM-07_16_03

Theory : reals


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